Do I need to post process my GPS data within a certain amount of time after collection? Do the services that provide the correction data to Pathfinder Office only make that data available for a certain amount of time?
This depends on the service. If you are using the CORS operated by the NGS, the NGS archives RINEX-2 files indefinitely, but individual CORS station operators are only required to keep their data available for a minumum of 30 days, (although typically they are available for longer than that). If the day you need is not available from a specific CORS, then you can download it from the NGS directly at NOAA CORS. As contrast, we run a base station and are a location provider for a private subscriber based network. Those files are only made available to subsribers for 30 days.
Most of the base stations that provide the files you use for differential correction are part of NOAA's Continuously Operating Reference Station (CORS) network. They keep files forever, but the quality is reduced after 30 days, I guess to save space on their servers. So the soooner you correct it, the better. Their full data retention policy is here: http://www.ngs.noaa.gov/CORS/data_policy.shtml.
Other base stations have different policies. If you are in the Trimble differential correction utility, in the "Select Base Provider" window you can click Properties and get the base station's web page, they usually tell you how long they keep the files.