Should Trump withdraw when he fails to reach 1237? The reason for a convention is to select a candidate who reaches 1237 on any ballot, not just the first one.
If Cruz stays in the race after being mathematically eliminated from the 1st round, it should be clear to all that his only reason for remaining in the race is to stop Trump. The GOPe have no intention of letting Cruz win the nomination and are just using him to stop Trump. They have said as much, and Cruz is smart enough to understand why the GOPe has temporarily coalesced around him and the role he is playing.