That is kind of strange behavior/
I have several 34410A and they all stay in Autorage mode, after pressing the button once.
I would try to remotely switch to resistance measurements and see if the problem persist.
Yes, strange.
Actually, the FW is 2.43.
You know what, try this:
select diode test and than select resistance mode, try that several times and check if instrument behaves normally. I have noticed that when i move from diode test to resistance, than is that strange behaviour more frequent. On the display says auto range, but i really dont know why the relay inside does not click when i short probes when in resistance mode, well that happens from time to time.
What do you think could be the cause of this behaviour?
Btw., in the meantime i have found this post below
read this:
https://community.keysight.com/thread/37599 same issue that i have!
Now i feel calmer

I am almost 100% sure that is a F/W problem.
Btw., do you maybe have 53131A counter? I have some issues with the counter. If you are experienced with repairing these units than you can maybe help me. Check my posts regarding 53131A.
Anyway, thank you for your reply.
Hrvoje