If the problem occurs on more than one instrument, it's unlikely to be an instrument problem.
If this were my problem, I would start by verifying that it really is due to late-eluters (as opposed to sample degradation). Do a single injection and wait; continue acquiring data for 10 times the usual run time.
If there *are* late eluters, then changing either the method (e.g., to normal-phase) or the sample prep (perhaps with solid-phase extraction?) is the "best" approach. The "band-aid" approach would be to run 5-6 samples (however many you can get in before the late peaks elute), wait for all the late peaks to clear the column, and repeat. This would obviously kill the throughput, but if it's a one-off or infrequent analysis, it may be more effective than validating a whole new method.
If there are no late eluters, then it looks like it's a sample degradation issue (confirm by prepping a fresh sample). In that case, I would address the chemistry of the degradation.