Is there a limit on the number of concurrent SMTP sessions?

[#1]

I'm the informal tech adviser for a friend's small business, which has a PlusNet business account.
There are now 5 (until recently 4) pcs in his office operating through their ADSL router. For historical reasons they all run Outlook 2003, using identical account POP and SMTP settings so that all email records are visible to all users!
Recently there have been problems with one machine not sending emails; relay.plus.net is visible but not accepting connections. I compared the failing machine's email and security settings with two of the working ones and they're the same.
While in the office (scatching my head) looking at the troublesome machine, it began sending. A few minutes later, one of the other machines which had never previously had this problem was rebooted and sending failed on it. This made me wonder if there is some kind of concurrent SMTP session limit being reached by these multiple, identical connections.
Of course, another point of commonality is the router, a Netgear DGFV338, but as far as I can see, it doesn't seem to be creating any restrictions on connections.

I welcome any inputs/observations.

[#2]

I'm not certain on the correct answer to this one but I've asked the Comms guru's to comment.

[#3]

I'll get back to you once I've got the definitive answer, as it's not one I know off the top of my head.

[#4]

After speaking to the Networks guys, they've confirmed there isn't a limit per IP on connections to relay.plus.net.
Can you try telnetting to the outgoing mail server on port 25 and pasting the output as a reply?

[#5]

Thanks for the feedback.
I'm waiting to hear from the office on whether the problem still persists. I'll try telnetting when I next go in, but that might not happen for a few days.