Part of the answer to the question of whether a civil suit can be reopened after it has been adjudicated depends upon whether one was the plaintiff or the defendant. If the plaintiff lost, he or she is prohibited under the doctrine of preclusion from bringing the same suit against the same defendant. Once again, depending upon the circumstances, once a final judgement has been rendered, the case is closed forever.
Defendents can usually have a case reopened on appeal. Assuming that no statute of limitations exists, and assuming the case was dismissed without prejudice, than it could be reopened. "Without prejudice" means the judge declined to render a verdict, leaving the case technically open, but dismissed for procedural reasons.
In short, an answer to the question is entirely dependent upon the circumstances unique to that case. It is possible to reopen a civil case that has not been adjudicated. If the there was a verdict in favor of one party or the other, it probably cannot be. If the individual wanting to reopen the case was the defendant, it is more likely to be reopened. Most importantly, however, is to go to trial having all relevant information and documentation present. As often as not, forgetting an important point and losing a case is simply bad luck, and a lawyer who did that would likely be fired and even be reviewed by the state board for attornies.
Unfortunately, you can't get two bites at the apple. Such is the nature of litigation. If evidence you thought relevant was excluded by the court then perhaps that would be an appealable issue. If it was an attorney oversight then perhaps there is an action against him or her. In a criminal trial against a defendant there might be a chance but in a civil case it is extremely unlikely. If a party neglects to introduce something they are just out of luck. Though as a practical matter, I would be surprised if that one piece of evidence would be enough to change a verdict. Unfortunately when one looses a case it is always the fault of the jury, the judge, either or both attorneys, the clerk, the tipstaff, etc.