Why couldn't they pass a single one of their many, previously-successful proposals under a Republican president?
The simple answer is that you're measuring "successful" by how many votes were garnered in Congress. This is a slippery measure.
Voting to repeal the Affordable Care Act when the sitting President (Obama) is guaranteed to veto your repeal is merely a political gesture. It says, "I abdicate responsibility for any negative effects of Obamacare, because I voted to repeal it!"
When the President (Trump) is actually likely to pass your repeal, then you can no longer just make political statements; you must consider the consequences more carefully.
This answer purposely does not address the question of whether a repeal would be a good thing or a bad thing in terms of economic consequences.
I only refer to the perceived consequences for political careers, as perceived by members of Congress. They may or may not even perceive them correctly; I am not judging that either.
Put another way:
Voting for a bill to repeal Obamacare that is subsequently approved by the President, puts Congress "on the hook" for the consequences of the repeal.
Voting for a repeal that is vetoed takes Congress off the hook for any negative effects of the Affordable Care Act.
One involves abdicating responsibility, the other involves assuming responsibility for potentially negative consequences.
That's politics for you.