This is happening indiscriminately on most series that we try to record.
My experience of the FVP-5000T is that it is reasonably reliable at recording a series. The first thing I would check is that the Humax is tuned correctly because if you are receiving from more than one transmitter series links will fail in a way that matches your description. I would do a manual tune using the following instructions:
1.Go to:
https://www.freeview.co.uk/corporate/detailed-transmitter-information and input your postcode and house number; tick the box marked "Detailed view".. Look carefully at the information returned for each transmitter; don't blindly accept the recommendation for the most likely transmitter.
2.Having decided on a transmitter, note down the six or seven channel numbers for the mutiplexes (shown in the column headed N and on a darker grey background) and carefully mark which one of these channel numbers carries the HD Mux.
3. On the FVP Menu, Settings, Channel Settings.
4. Select Automatic search for channels and immediately stop it; save the results. This deletes all previously found channels.
5. Select Manual search. In the Channel field press right arrow, scroll up or down and select the first channel number from your list. In the Transmission field leave it on the default DVB-T for all channels except the HD channel; for the HD channel it must be changed to DVB-T2. Press Search. This should find a number of channel names. Save the results.
6. Repeat the manual search for each channel previously noted.
7. You will then need to re-enter your schedule of recordings.