What kind of port? If you are talking about "virtual" ports..ie..http running on port #80...it would depend on the setup of the vps.
If you have a xen or vmware vps...I have no clue.
If you have a openvz or virtuozzo vps..login to your vps..cd out of your root directory...and type:
The resource you are looking is (I believe)
NUMTCPSOCK (For TCP sockets)
NUMOTHERSOCK (For other socket connections)
If you see a number in the last column (Failcnt)..your vps has indeed reached the maximum number of sockets allowed...and connections have failed.
Feel free to post further if this does not help.
Bryon L Harvey
Soil Relocation Engineer