Yes it could if they voted to disqualify him in the penalty phase. However, since impeachment is associated with an actual trial in the Constitution (for example specifically cannot be pardoned) there might be a double-jeopardy issue. Also, matters not resolved cannot carry over from one session to the other so it is either resolved finally or there are no impeachment charges to consider. Lastly, there would be a major issue with the jury (Senate) not being those present during the trial. What would you say if you were being held on trial and when it came time for the jury to deliberate they seat 12 new people?
Ultimately, SCOTUS would pick any number of reasons to say that a revote on impeachment charges under these circumstances is invalid.