Normally I would expect that the update would fulfill, but it doesn't work. I've tried this on numerous versions, and different methods and it always fails.

Tell us what happens instead
Operating system: Windows 10 Pro Insider Preview Build 16251.rs3_release.170721-2122
Version of Telegram Desktop: 1.17
Used theme:N/A
Logs:
Insert logs here (if necessary)
@cooperpellaton Some process (antivirus or smth) is locking the "Telegram.exe" file and it can't be overwritten :( It doesn't reproduce when I update, it updates fine.
works for me(TM) too.
Microsoft Windows [Version 10.0.16257.1]
same issue
I suggest you to get https://lockhunter.com/ to see what's locking the file to see where it's the issue.
I'm getting this as well.
Lockhunter just says it's locked by System. This is happening on two separate machines and the locking started at the same time. Can update by downloading the installer but that's a bit of a faff.

Also worth noting it cannot unlock the process.
Ok, it looks it's windows bug and not telegram bug:
https://stackoverflow.com/questions/4378192/windows-2008-r2-kernel-system-process-pid-4-is-locking-files-and-folders
https://www.ryadel.com/en/unlock-file-handle-locked-system-active-process-windows/
https://social.technet.microsoft.com/Forums/windowsserver/en-US/b9ee9739-8ac8-4c83-8bff-1a573d1c5979/windows-7-system-locking-my-files?forum=winservergen
logout from your user and login again and click update as workaround to this windows bug.
Most helpful comment
logout from your user and login again and click update as workaround to this windows bug.