Pizzaguy knows.

I was in your same situation a couple of years ago. I was manually putting the top up and down until I figured out that the two main lifting cylinders were leaking. I had TopHydraulics rebuild just those two and it worked great. I haven't had any trouble since then and I had completely forgotten many of the same issues that you're talking about when manually raising and lowering the top.

Looking back at a post I made in 2018, I said:

I have been leaving the engine on when moving the top up and down. As PizzaGuy says, it keeps the control system for the top knowing where the top is. I used to move the top up or down with the engine off and eventually, the control system got mixed up and I had to re-sync it.

I've added one more step to the manual process. After I finish the up or down process, I turn the engine off. I leave the engine off for two minutes. That seems to be the amount of time it takes the control system to go to sleep and the light on the power-up-power-down switch to go out. Once it goes out, (and it always seems to be right at two minutes), then it stays off after I start the engine up. I don't get any beeping at all following that system.

That might be worth a try. I don't know why it worked for me.

The other two questions:
1. Are you manually raising and lowering the top with the engine on?
2. Have you tried re-syncing the top following Pizzaguy's process of doing three complete cycles of raising and lowering the top with the engine on?