[wrxtasy]

With my Minix remote it seems that it does sleep, the first button press never works when it has sat for a minute. I just press it twice. 

I bet you have the A3 or a new key backlit MINIX Remote ?
That is the annoying behaviour of those remote and why they should be avoided.

Unless you are telling me the old faithful A2 lite now has that stupid battery saving technology as well in some newly released model ? 

I bought a A2 Lite like a week ago and well since I asked about it, yeah I guess they added the battery saving to it. The first button press never works

Jeez that's disappointing!
I will take it out of ALL my recommendations posts now...

MINIX are Bloody idiots - they have taken a great working product (the original A2 lite remote) and added battery saving stupidity too it !
Batteries lasted 6+ months in the original A2 lite anyway.

With the Minix Neo A2 I often have to press multiple times buttons for it to register, does the remote go to sleep or something? Is there anything I can do to improve it?

Jump on the MINIX forums and complain LOUDLY - two button pressing after you pick up a remote to be able to use it is frankly utterly stupid.
I would send it back from where it came from saying it is broken and ask for a refund or buy one of those WeChip G20 remotes.