Thanks for your bug report. I have not been able to reproduce this issue yet. I followed your steps (running under Windows 7) and at step 6 I opened Firefox at imgur.com and opened 30 separate imgur.com images (Firefox is taking a long time to load them all and is still loading after five minutes...). mIRC was flooded off Freenode (after using /amsg) and reconnected without any issues. I tried flooding myself off a few more times and mIRC reconnected every time.
Have you experienced this issue before with previous versions of mIRC?
Are you running any other applications in the background, such as anti-virus or security software?
If you restart your computer and try again, do you see the same issue?
The only reason you would see this message, that I can think of, is that there is a Windows/Winsock memory/socket/port resource issue. For example, Task Manager and TCPView are showing me that with 30 imgur.com image windows open, Firefox is using almost 1 Gigabyte of memory and 400 socket connections. It is difficult to say what kind of effect this would have on other applications that are trying to make persistent internet connections.