Co-founder performance in the startup has dropped. He clearly has other priorities in his professional life, like other startups, and he doesn't want to give up his 30% shares.
The only written agreement was an email exchange agreeing on the ownership split, and the work to be done...but maybe it was too vague, without the hours that were supposed to be invested by both parts, for instance.
How to deal with this situation?
If you have no legal agreement that specifies what happens in this case you will need to do several things:
First: Offer him a fair price to buy out his shares.
If he does not accept:
Or, sell the company to another entity for a fair price. (You own the new company.) Give him 30% of that sale.
And never enter into a partnership or start a new company without a written agreement that covers all your bases.
You should read the agreement of partnership and act based on that. If the shares aren't vested - you can reclaim the non-vested portion if the vesting conditions are not met. If the partner is not only a shareholder but also an employee - you can fire him to stop paying salary. In any case - get a legal consultation first.
If the documents surrounding his share issuance don't provide for any sort of buy-back or vesting, then there's not much you can do to take them back. Does it matter? The other two founders have a majority of the voting power. Over time, those two founders will have other opportunities to take shares and to dilute the first guy down.
Alternatively, if the existing company hasn't created any assets, then start a different company without him in it.