Hi,
It is hard to say what exactly the cause of your problem is but here are a couple of suggestions:
1. Check how many user license do you have on the PIX? It is either 10 or 50. If it is 10, then you might be running out of licenses. I had this problem when I had 7 users and a few servers on the network.I did not realize that PIX count each connection through the device not user's. From then on, I always bought the 50 user license.
2. When the outage occurs, terminal into the PIX and make sure that you are able to ping Internet and the inside network. I also suggest that the outside address of the PIX is a static not DHCP.
Hope that points you in the proper direction.
Kersean