Most of my scripts use persistent connections to a mysql or postgresql database.
That is your problem.
Don't use pconnect to databases with CGI, use it for Apache only.
There really is no need for a pconnect anyway, since each time you call a connect, it just uses the last resourceID provided.
And besides, you should have DB wrappers that check for an active resourceID to avoid trying to reconnect.
And, running PHP as a CGI will be slower than the Apache Module version, due to the fact that Apache must exec your script as an external process, capture it's output and then display it to the page, so yes... there will be a performance hit.