I heard somewhere that 1000's of things have been proposed as amendments, but only the 27 ones we have actually passed. If 1000's have been proposed, then I'm sure most of those just immediately got shut down or so. But some have to have reached the later stages without passing, right?
In 1791, the proposed Congressional Apportionment Amendment came within one state of ratification. That is the closest for an as-yet unsuccessful amendment.
The era (equal rights amendment) came within 3 states of being ratified. It could still become law one day.