There is no statute of limitations and no procedural bar based on time. Clinton was impeached in the 105th Congress and tried in the 106 Congress. Time lapse was a few weeks on the calendar, Christmas recess, and about three days of session.
The House adjourned sine die the same day it impeached Clinton. Managers were sent to the senate the second day of the next Congress.
Standing house rules contain nothing on impeachment. senate rules on impeachment start with reception of the impeachment managers.