A couple of things.
1. Make sure you have the option to keep 1Password mini running, seems you already have that enabled
2. If you have too many apps running in the menu bar, you will have many apps fighting for space. Notably you'll see this happen because the menu bar is "split" between the menu items for the app (File, Edit, View, Window, Help, and any other specific to the app) and the menu bar icons on the right. The menus will have priority so that they are displayed, this means if you have an app with a lot of menus it will push other icons (from the right) off the screen and they will appear to be invisible. Your best bet is to simply make sure you aren't running so many menu items on the right. Disable those that you do not use frequently. Many people used to use an app called Bartender for this but it now requires disabling System Integrity Protection so I know people are more hesitant to use it. But it is an option if you want to disable that security feature.
I suspect you're encountering #2 there. This can be compounded by low screen resolution, so on older computers with lower resolutions, or with newer devices that have retina displays when the scale factor is cranked up too high it can reduce the amount of space menu bar items and menus have available to them.
We don't have any control over this either.
A third possibility is that the mini is crashing, you'd usually see this as the mini appearing, then disappearing, then reappearing again (as it relaunches automatically). It's position in the menu bar may change as well if other apps have been launched since it was originally launched. Something to look for at least. If you can trigger this reliably, you can test for the crash situation really easily by simply opening 1Password, unlocking it, then triggering the issue. If you then click 1Password again and it's locked, this indicates that the mini crashed. It holds the unlock/lock state and when it crashes it will lose the memory where the decryption keys are stored and then when relaunched require re-entry of the Master Password.
Hope that helps, but if you want support with 1Password this is a 3rd party support forum, you may be better served by asking in our own
support forums where we have support personnel answering user questions. I read these forums and try to respond but it can often get lost in the clutter, I just happened to stumble on your question today.