Error 17832: Unable to read login packet

Client of mine has a major problem with the Error 17832 (accompanied by 1608) on MS SQL
Server 6.5 running on NT 4.0 SP3. SQL Server has 100 per-seat licenses.

Application, running on the client computers, establishes several connections (I know...) to
the SQL Server on as-needed basis. The errors started to come up when application has
executed on 40+ workstations. When the "saturation level" is reached, no connection to the
SQL server could be established (even for Enterprise Manager, running on the same NT box!)

Any suggestions? Licenses, network, client configuration, SQL Server configuration...
Your suggestions sent to vadim@prosysllc.com will be appreciated.

Thanks,

Vadim Brusilovsky