Not necessarily. Either body can still take up a bill again as long as the session has not adjourned. In fact, bills are technically alive over the course of a biennium so a bill that was introduced in the first year (odd year) of a biennium and didn't pass, it could still be discussed until final adjournment in the second year (even year). When a bill fails to get the required number of votes, the author can try to persuade other members to change their opinions on the measure. The only way such a bill can be taken up for a vote again is if a member who voted against the bill is willing to make a motion for reconsideration and the body agrees to reconsider.
In addition, many bills that either don't receive a floor vote or are voted down on the floor end up as amendments to other bills of similar topic.