Short answer. Only if the certificate allows it. Under Article 1850, general partners have no authority to continue the business with partnership property after a general partner dies unless the right to do so is given in the certificate. If the certificate is silent, they need the written consent of all the limited partners.
What the law says
Continue the business with partnership property on the death, retirement, insanity, civil interdiction or insolvency of a general partner, unless the right so to do is given in the certificate.
Civil Code, Article 1850 — Powers of a General Partner. Read the full provision →
The death of a general partner is a turning point
A limited partnership leans on its general partners to run and be liable for the business, so the loss of one is treated as a serious event. Article 1850 lists continuing the business after such a loss among the acts a general partner cannot simply decide alone. The exact wording bars the general partners from acting to continue the business with partnership property on the death, retirement, insanity, civil interdiction or insolvency of a general partner, unless the right so to do is given in the certificate. Death is only one of several triggering events; retirement, insanity, civil interdiction, and insolvency of a general partner are all treated the same way, because each removes a person the structure depended on.
The certificate is the key
The phrase unless the right so to do is given in the certificate is what decides your question. If the partnership's certificate — the founding document that defines the limited partnership — already grants the remaining general partners the right to carry on the business after such an event, they may do so, and no fresh consent is needed. If the certificate says nothing about it, they lack that authority by default. This is why well-drafted certificates expressly provide for continuation: it lets the business survive the death or withdrawal of a general partner without grinding to a halt or requiring everyone to be gathered again in a crisis.
If the certificate is silent
Where the certificate does not grant the right, the general fallback in Article 1850 applies: the act requires the written consent or ratification of the specific act by all the limited partners. That means unanimous, written agreement of every limited partner, given for that particular continuation. A limited partner who invested on the understanding the venture would wind up on a general partner's death is protected — his consent cannot be assumed. So the practical answer is to check the certificate first. If it authorizes continuation, the remaining general partners may proceed; if not, they must obtain the limited partners' written consent before keeping the business going with partnership property.