I doubt this is old age (either the Humax's or yours).
This sounds like a problem that occurs on some of the minor channels. The actual time that something is broadcast seems to slip. Just a stupid question first. You arn't recording off ITV3+1 by mistake? That will cut off at midnight anyway.
The only suggestion I can come up with, not knowing how you set the recording in the first place, is to manually reset the time of the recording.
If you are only having problems with this programme you could try this.
I'm sure there will be many critics to what I suggest but what I would do is...
(You will probably have to cancel the existing settings first)
Go to the guide (press guide on the remote) followed by find (blue button). Enter "Order" and Find. Scroll down to the first Law & Order Uk on ITV 3 and select. Answer OK to the "Do you want to reserve" question, BUT "One Programme" to the Series Link question. Press back twice (you should be at the Guide screen) Press yellow (schedule) and find the Law & Order you just set - click OK. Change the End time to 23:05 or later (right arrow next to OK will do this). You may want to change the start time to earlier also( left arrow) ? Change Repeat to Weekday (right arrow) and save.