Short answer. When three conditions are met. Under Article 1857, a limited partner gets his contribution back only after the firm's outside liabilities are covered, all members consent, and the certificate is cancelled or amended. He may rightfully demand it on dissolution, on a date the certificate fixes, or after six months' written notice.
What the law says
a limited partner may rightfully demand the return of his contribution: (1) On the dissolution of a partnership; or (2) When the date specified in the certificate for its return has arrived
Civil Code, Article 1857 — Return of a Limited Partner's Contribution. Read the full provision →
Three conditions before you can withdraw
Getting your capital out of a limited partnership is not a matter of simply asking. Article 1857 sets three preconditions that must all be met before a limited partner shall... receive from a general partner or out of partnership property any part of his contributions. First, the firm's outside liabilities must be covered: all liabilities except those to general partners and to limited partners for their contributions must be paid, or enough property must remain to pay them. Second, all members must consent — unless the limited partner is entitled to demand the return without it. Third, the certificate must be cancelled or amended to record the withdrawal or reduction.
When you may rightfully demand it
The article also fixes when a limited partner can actually insist on the return, subject to those conditions. A limited partner may rightfully demand the return of his contribution: (1) On the dissolution of a partnership; or (2) When the date specified in the certificate for its return has arrived, or (3) after he has given six months' written notice to all the other members, if the certificate fixes no time for the return or for dissolution. So there are three moments: the firm dissolves, a date the certificate set arrives, or — where no date was set — six months after he formally notifies everyone.
You get cash, and can force a dissolution if refused
Two further points round out the picture. Unless the certificate says otherwise or all members consent, a limited partner has only the right to demand and receive cash in return for his contribution. And the article gives him a remedy if he is wrongly refused: a limited partner may have the partnership dissolved and wound up when he rightfully but unsuccessfully demands the return of his contribution, or when the firm's other liabilities are unpaid and its property is insufficient to cover them while he would otherwise be entitled to a return.
Planning your exit
If you are a limited partner wanting your capital back, the practical route is to check what the certificate says about timing first. If it fixes a return date, that is your entitlement when it arrives. If it does not, you can trigger a return by giving six months' written notice to all the members. In every case, the firm's outside creditors must be provided for and the certificate updated before the money can move. Expect to be paid in cash. And if you make a rightful demand and are refused, you are not stuck — you can seek dissolution and winding up.