The disadvantages with using a TPA for COBRA administration, particularly one who really has their act together is complacency. Our complacency!
We have used a TPA (COBRAServ) for four years and, while it seemed expensive initially, we are more than satisfied. We have rationalized the cost by determining how many exceptions we did not make that would have turned around and bitten us on the behind.
When we resolve issues, questions or disagreements, we nearly always determine that the TPA was correct, and we were wrong or the error was on our part. (Our HRIS system frequently misses ee's with qualifying events. With 6,500 FTEs and a 25% turnover rate, we have a lot of them.)
Before we contracted with COBRAServ, we used a local TPA for two years - which was a disaster. I compare it to my trying to coach the Redskins. I know all the rules, but I'm not qualified to run the team.
Good Luck!