does it cause any problem to our website if we got banned in any forums with our signature back links..?
Anytime you lose backlinks is can have a negative effect on rankings (assuming they were do-follow links).
The answer is no, it does not effect your ranking. Some forums take away the signature of all banned members while others do not. Anyway, do not do anything that will get you banned!!!
If you have been banned but all posts with signature links made by you still exists - No. / Opposite - Yes because you lose backlinks.
Let me clear up the replies in this topic as they seem very vague and confusing to a newbie. If only your profile has been banned but the topics & sig links still remain ... then no, there'll be no drop. If your profile has been deleted AND your messages (and therefore backlinks are gone) ... then yes, that could cause a drop. However signature links are nofollow for a large number of forums, so you were never getting a boost .... and even if they are dofollow, forum links have an incredibly small value in terms of ranking.... so you may drop 1/2 places but nothing significant. Possibly the most important question to be asking is why you got banned so that it doesn't happen again.
So far I dont think there are any issues with an account and a site signature. But better stay safe and dont get banned.
It depends on how many links you lost. As stated previously not all forum will delete accounts / posts after banning, which means the links will still be active. If the links are no-follow and removed you probably won't notice any real change in SERPS. If the links are do-follow and removed you probably will notice a change, especially if you lost a lot of links.