I have seen several posts referring to the same failure message on upgrades, but none so far with 3.2.4 to 3.2.7 upgrades.
The error still exists.
The installer detected a timeout
The installer has detected a timeout, you may try to refresh the page, which may lead to data corruption. We suggest that you either increase your timeout settings or try to use the CLI.
I have found references to max_execution_time, and a recommendation to up this. However, the error came after my forum was put into maintenance mode while I secured the files and database, then uploaded the upgrade files. This took a couple of hours, after which I got the error in the upgrade. To get the forum back on-line as quickly as possible I re-instated the securities, then started looking for the answer to the problem.
It would surely be wise to mention in the upgrade notes that the possibility of this timeout exists, so that the max_execution_time can be checked before the upgrade attempt.
It's a poor day when you don't learn something!