It should not stop transferring because it thinks its running out of space on the Tivo. What the Tivo does, is it would start clearing out the space needed for the next recordings, first from the Recently Deleted folder, then the suggestions (if any), then finally the recordings.
If it stops transferring, its probably because your computer's hard drive is getting filled, not the Tivo's.
I would use KMTTG, which does more then just download recordings, it also decrypts (removes the Media Key layer), plus other things along with remote functions. It also can read things like how much space is available.
Original S1 (Recycle Heaven)
Series 2 (PLS, sold)
TiVo HD (XL, PLS, "652")
Juliet Basic (4XL, PLS)
The TiVo Apocalypse begins on Sat 2013 Feb 16 00:00 GMT!