Do the big donors to a losing US presidential candidate ever get their money back? And if so, how, and in how much time?
There are no refund requirements
The Federal Election Commission oversees national elections. They have compiled the various election laws in a single document. I've read some of these laws, searched for things, went through the index, and more - and have found nothing about any situation where refunds are required for campaign donors - whether they win or lose.
Refunds may be optional
However, candidates may refund money at their own discretion. Back in 2010, ABC had a story about the sudden rise in refunds of campaign contributions for various reasons. Generally, these refunds were because candidates had accepted money from organizations who made them look bad (for example, some of the refunds were connected to large banks after the banking collapse).
The same ABC article mentions a law requiring candidates to refund contributions if they drop out before their primary (or caucus). This is because the election laws define elections as being federal elections (general, special, run-off, etc.) and primaries. If you accept campaign contributions and don't actually participate in an election, then you don't have a lawful usage of those funds.