An additional reason appeared when I started researching the topic.
Apparently, Windows 10 no longer even creates the recovery partition during installation!
The entire WinRE is now stored on that same system reserved partition, which contains your window’s BCD!
The recovery partitions should only be present on Windows 10 installations which were either upgrades from a previous Windows version, or (as in my case) were installed within about 6 months after Windows 10 became available.

These instructions are also useful if you wish to increase the size of your system reserved partition – for example, if Windows 10 updates are failing because of that partition’s lack of free space.

WARNING: changing partition tables on your hard/solid-state disk may easily result in complete data loss!
Instructions below are provided as-is, to be used at your own risk. See full disclaimer on the About page.

WARNING: although it is also possible to merge the system reserved partition and windows 10 partition (so that the entire Windows 10 uses only 1 primary partition), I do not (and will not) offer instructions to do so. In fact, I recommend that you don’t merge the system reserved and windows 10 partitions.

Merging system reserved and recovery partitions, step by step.

1. First, we need a convenient partition manager; I have used a free MiniTool Partition Wizard, but other great free partition managers (like AOMEI Partition Assistant and I guess a few others) should be sufficient for us. Download and install one of those. It is impossible to use Window’s own Disk Manager for the steps below.
2. My starting state is this:

   [ 189MB free space ] [ system reserved, 100MB ] [ windows 10, 100GB ] [ recovery, 450MB ] [ free space ]

3. Your starting state may look a bit simpler, like this:

   [ system reserved, 100MB ] [ windows 10, 100GB ] [ recovery, 450MB ]

   Presence or absence of free space at the beginning or end of the disk should not make any difference (unless your windows partition has very little free space).

4. Our goal state is:

   [ system reserved, 900 MB ] [ windows, 100 GB ] [ free space ]

5. Create a full disk backup! Yes, I really did that. I can highly recommend booting into Clonezilla (or your Linux, if you dual-boot), and performing a full disk-to-image backup. If anything at all goes wrong – you should be able to completely restore your system to the previous functional state.
6. Verify that your full-disk backup can be restored (is readable/decompressible/whatever). Clonezilla has an option (enabled by default) to perform this check after disk imaging is complete – this was sufficient for me.
7. Verify that you have a functional WinRE: start Administrator CMD (or PowerShell), and run reagentc /info – it should tell you that WinRE is enabled, and also tell you that it’s using partition 3. I’d also strongly suggest that you create a separate bootable USB with WinRE – Windows 10 has its own tool to do so.
8. (optional) If you, like me, had some free space at the beginning of the disk, before the system reserved partition – then it makes sense to first extend the system reserved partition there. Use your partition manager to do so – either as a one-click Extend partition operation (and then select the free space upstream, all of it), or as a Resize partition to move the left edge of system reserved to disk’s beginning. Reboot. This worked flawlessly for me. If your Windows 10 does not boot anymore – try fixing boot using your bootable WinRE, or the WinRE on your disk. If that fails – restore your disk backup, and look for a different solution…
9. When merging system reserved and recovery partitions, one has to keep in mind the free space requirements of these two partitions (for UEFI, for MBR). They are a bit weird, so I picked 900 MB as the target size for system reserved; with this size, at least 320 MB have to be free on that partition after we are done. After merging the free space (189 MB) and the sysres partition (100 MB) I already had 289 MB, and needed to add (900-289=) 611 MB. Start your partition manager again, Extend system reserved partition using your Windows 10 partition, and reboot again. If there is no option to extend: first shrink the windows partition from the left edge by the calculated number of MB (611 in my case), then extended sysres partition into the freed space – and reboot. After this step, the disk should look like this:

   [ system reserved, 900 MB ] [ windows 10, ~100GB ] [ recovery, 450 MB ] [ free space]

10. Now we are going to move the WinRE from a dedicated partition to a sysres partition, in a few easy commands. Start Administrator CMD or PowerShell, check that your WinRE is still active: reagentc /info. Now disable it: reagentc /disable. Verify with another reagentc /info. If disabling failed, and you wish to have the WinRE functionality – do not proceed! I have no idea if proceeding after failure here would result in a functional WinRE. Do not reboot, keep the CMD/PowerShell open!
11. Delete the recovery partition, apply changes, do not reboot! (although it should actually be safe to…)
12. (possibly optional) Create an unformatted placeholder partition where your recovery partition used to be, to prevent Windows from creating it again when you re-enable WinRE. In my case, disk layout after this step is:

    [ system reserved, 900 MB ] [ windows 10, about 100 GB ] [ Unformatted primary partition ]

    Do not reboot.

13. Back to your elevated privileges CMD/PowerShell window: simply run reagentc /enable, and confirm with reagentc /info. As there is no other place to put WinRE now, reagentc should save it to the (now big enough) system reserved partition.
14. Delete the placeholder partition. Your final state should be similar to:

    [ system reserved, 900 MB ] [ Windows 10, ~100 GB ] [ free space ]

Congratulations, you have just successfully merged the system reserved and recovery partitions of Windows 10!

If not hardware, but “only” software is malfunctioning – try SystemRescueCD, a Linux-based recovery CD/DVD/Flash stick (it all depends on how you burn/install the downloaded file – manuals and how-to’s are available).

As always, Disclaimer: I am in no way associated with SystemRescueCD, and gain no profit from this post. Any advice I give is provided AS IS, with no guarantees of fitness to your exact case.

It does exist – Ultimate boot CD. That CD has numerous freeware testing and diagnosing utilities which will help you – if you are up to some good old (read “small fast”) DOS utilities. And not that old, actually – modern hardware is supported.

The only modification I’ll do to the Ultimate boot CD will be adding freeware bin/hex viewer/editor. Surely, more utils to come – with original size of just 115MB, there’s plenty of room to add extensions. You can even extend the CD image with non-free software, like Partition Magic.

P.S. To diagnose and fix software problems – have a look at System Rescue CD.