Sorry to hear you're experiencing issues with your series links, Josh_RW is away at the moment so I'm just stepping in if that's okay.
I would just like to check if any of these Series Links that are missing/part recorded are showing up in Recording Hiccups?
You'll find this option in -
Home - My Shows & Recordings - Recording Hiccups.
Also another good place to check to make sure there is nothing clashing with your recordings and cutting them off when they start/finish is manage my series links which you will find in -
Home - My Shows & Recordings - Manage My Series Links.
If you see anything greyed out here it normally means that it isn't going to record for one reason or another and you can even priorities your series links to make sure another recording doesn't interrupt them by highlighting the up/down arrows on the right and moving the series link right to the top.
I hope this helps, let us know how you get on or if you have any further queries.