What should we do about a co-founder who discontinues his work in the startup?

While you may have a difficult time wresting or otherwise compromising a shareholder's capital contributions (or equity directly tied thereto), a manageable way to hedge against the risk of an uncooperative co-founder is to tie vesting of a substantial portion of his equity to performance, e.g., via a Management Equity Agreement ("MEA") that is periodically reviewed by the founders. An uncooperative founder, responsible under the MEA for some level of contribution or time spent, can be found in breach and thus forfeit subsequent equity from vesting. Schedules and other terms by which vesting would occur will need to be negotiated, of course, and even if the facts of your particular situation warrant another framework, it is very advisable to contact local corporate counsel to explore specific paths forward.