It should remember the time period you last selected. It is not security specific so whatever you change it to would apply to all securities. So, if you select 5 yrs for one security, it will be 5 yrs for all securities. And if later you select 1 yr for a different security it will be 1 yr for all securities.
Let me know if this answered your question. If it doesn't, we can troubleshoot other things that might be changing your last time period setting.
Ah, I get it now. I was able to replicate the issue you are seeing:
Seems like this might be a bug. I suggest that you report it to Quicken via Help > Report a Problem. You can copy/paste the URL for this thread into your report. This process kicks the report directly to the engineering team at Quicken. I will do the same.