Do you make use of Collector groups by any chance? Are both Collectors accessible when the agent is started/restarted? I had an issue recently where the one Collector instance, which is part of the two Collector instance group, wasn't available and the collector list file had this 2nd instance as the first entry in the file. This means the agent tried to connect to Collector instance 2, which fails eventually and then successfully connected to the 1st instance, but by that time the Windows service timeout was reached and the service doesn't start with that same error you're getting.
You can increase the timeout, but the root cause would still not be resolved i.e. in my case, the root cause was an inaccessible Collector instance.