The builds expire to force you to keep up to date. Despite Bigstar's best efforts, betas have bugs. Forcing users to keep up with current builds will save you problems in the long run, as running a buggy copy of FlashFXP will only cause problems. And the fact that it expires soon can only mean there's a new build coming sooner
To limit download or upload speeds:
Options --> Preferences (or F6)
go to the Transfer tab
check off "Obey download speed limit" and set a max transfer speed (in kilobytes per second).
(you can do the same for upload speed limit)