This is what my host adminitrator said to me:
"Mostly you are noticing the problems now
because another of our clients (who regularly gets a lot of hits) decided
to try mysql_pconnect too. Basically for each client who uses pconnect
you get numclientsnumsustainedhits connections to the database. So if 1
person is using pconnect, that equals roughly 150 connections to the
database. If 4 people (lets say *, *, the client I
mentioned above, and one other), then that means 600 connections to the
database (plus the regular 50 or so that the connect version could be
using at any given time). Now lets say that our new high performance
servers spike up usage to 300 http connections every so often. (150 is
about average normal simultaneous connections to our servers) At 300
apache processes, and connections to 4 databases, that totals 1200 (for
the pconnects, +100 from the connect versions). Mysql itself is only
capable of 1024 connections (or at least ours crashes if I try to set the
limit higher). So it stops working."