Returning to the main menu does not affect the timer in my experience.
However, I have noticed being allowed to take an extra batch whenever I gain a power play rank. So the timeline goes something like this:
- Take batch 1. (timer starts; not allowed to take more)
- Do activities that raise my rank.
- Take batch 1a. (timer is not reset; this is an extra batch; not allowed to take more than one at this point)
- Wait for original timer to expire at 30m.
- Take batch 2. (timer now resets)
Batch 1a only seems to be allowed if I rank up before the timer expires. If I don't take batch 1a before it expires, I am still allowed to take the extra batch when I eventually visit the power contact, making it appear like I'm being offered a double batch.
My guess: Allowing us an extra batch on rank-up might be deliberate, to account for the fact that some ranks increase our batch size allowance. When we reach such a rank midway through a timer, it would make sense to give us the difference between the batch size we last took and the size we are now allowed. Just giving us an extra batch instead might have been easier for the developers to implement.