Why don't you turn it on when you are ready to take the bike outside?

What sensor or sensors are you having trouble with? With my Garmin Edge 530, if I start my timer before waking up my Di2, then I have to stop the timer before it will find my Di2. I don't know why, I haven't seen any other complain of that. However, I've also made it a habit to wake up the Di2 when I turn on my Garmin just before going outside with the bike.

It's rare that any other sensor gives issues pairing. But usually when they do, it's after a update. But turning the device off and on or doing a reset will have it all working correct again.

Another option might be to just start the timer when you turn on the unit. If you have auto pause enabled, then the timer won't get but a few 0.01'ths of a second on it. But since the timer is started, it shouldn't turn itself off. Be sure to wake all the sensors on the bike at the same time too.

You really should call Garmin Support and tell them that you have trouble with the sensors staying paired. They'll work with you to figure it out. Older Garmin's might need a extra step that you may not be doing correctly. Or perhaps you got a dud.