Maybe a system that better reflects social status, connections and authority at the site to replace the "recruit new sleepers" system? Of course, since several Liberal Heroes can be sleepers in the same facility and help each other build trust, I suggest that an infiltration value is given to each site as well as to each liberal there. Different infiltration ratings could offer different things: Map at 20%, all doors unlocked during raids at 40%, the ability to have sleepers shut the facility down at 95% and something like that. There could also be generic benefits from increasing site infiltration ratings: Longer time before massive conservative response, more effiecent promotion of liberalism, sleepers more unlikely to get caught, possibly diversions and other neat stuff. It would really be nice if sleepers had more to do with raids than just reveal the map or occasionally open the club door if you ask me.
I'd imagine this would work like this: Each location has 0% infiltration if no sleepers are there. Once sleepers are in, they can start "Build connections" or something, mingling with the people in the facility. This would gradually increase infiltration level, and if the sleeper is well respected (high personal infiltration%) this would be a lot quicker. Multiple sleepers of course can form ties more effectively. Infiltration% will lower from high security and getting closed down, as well as everything else suspicious that happens, but by building connections the sleepers can quickly ensure their conservative "friends" that they are trustworthy. Site-based infiltration is downed to 0% when there are no more sleepers there.
If this site-based infiltration is implemented, please make it able to take out CCS too! Of course, it takes ages to build a strong enough network within such a conservative organization.