I would rule that charm person does not require concentration. However, a natural "20" always succeeds for saving throws (in my games, at least), so your warrior would have a 5% chance of throwing off the charm every two weeks.
Were it my game, I would allow the wizard to continue attempting to solve his problems with charm person, making note of any Mercurial Magic or manifestation, and being fully aware that in DCC there are often "tells" that a being is charmed, which other beings can pick up on.
Then you have two jobs, IMHO.
(1) Consider who...or what...notices, and what they will do about it. Possibilities include the patron of a charmed wizard, another wizard who wants the PC's power, a demon, or even a deity concerned enough to send a cleric on a divine mission. +2d30 if you can manipulate it so that the cleric entrusted with such a mission is another PC.
Remember Gandalf's reluctance to start a fire with magic on Cadharas because it would be noticed? What this PC is planning/doing is far more noticeable. Simply have the world react as it should. Read some Clark Ashton Smith, H.P. Lovecraft, or Lord Dunsany for ideas.
(2) Make sure that, sometimes, what appears to be the "boss monster" isn't the last, or even the biggest, threat. Hell, throw whole adventures at the PCs while the wizard is still suffering from spellburn. It's the right thing to do. A smart foe, especially a smart demon or a rival wizard, would wait until the PC was at his weakest before choosing to act. Jack Vance can give you some ideas about this.
In any event, as the PCs become more and more powerful, you should be fine with the wizard charming the common rabble at his convenience. After all, natural "1"s are inevitable, and Luck eventually runs out.
Cathbad the Meek (herbalist Wizard 1): AC 9; 4 hp; S 7, A 7, St 10, P 17, I 13, L 8; Neutral; Club, herbs, 50' rope, 50 cp; -1 to melee attack rolls. Hideous scar.