i've installed and removed several aftermarket alarms and never once come across a problem with the base unit losing the remotes. they usually work on a standard rolling code setup where each time you press the remote button it sends the next code in the sequence. the sequence will be made up from thousands or millions of codes. to make sure the remote and base unit remain paired there is a 256 code allowance, so you can press the remote up to 255 times with the base unit unpowered and it will still work. the base unit's memory will keep the last received code even when power is cut for some time, and will accept any code up to 256 after than in the sequence. every time the remote is used the code marker in memory is changed to keep the remote and base unit paired. i've had alarms sat in my garage for years and they still worked again first time.
sometimes if the remote's battery goes flat the remote will forget which code it was previously using. this will force it start at the beginning of the code sequence again. this doesnt happen on all remotes, but it happens on many of them. when this happens you need to reset the base unit so t it will be again paired with the remote. how you do that depends on the base unit. on many of them you need to press a button, or swap the live and earth, or remove a small watch type battery from inside for a few minutes.
