How do I make Talvas Fathyron stock up his merchant inventory?

As quoted from the Skyrim Wikia page on Talvas Fathryon:

Talvas may stop selling goods including spell tomes. Cause unknown but may have to do with using him as a follower. This makes any spells that can only be bought from Talvas unobtainable. This can never be resolved on consoles making it impossible to buy his unique spell tomes.

This implies that if you are playing on the PC you can obviously gain these items via console commands.

The Talvas Fathryon Talk Page over at the Unofficial Elder Scrolls Pages has the following little tidbit by the user MadAndyD:

Though Talvas fulfills all these roles, he seems to do a poor job of multitasking. He only trains and sells whilst in the proximity of Tel Mithryn, but, it seems that even when in the proximity of Tel Mithryn, as a follower he cannot sell, with the relevant window instead showing his inventory, as if you were to trade with him. However, dismissing him did not seem to instantly fix his merchant screen, nor did waiting for his stock to reset, I was only able to fix this by recruiting another follower altogether, and then visiting him.

Give it a try.