Tough question to answer, but since ECMO is not an easy & cheap option to implement I'd say financial constraints come to mind inmediately, specially when cardiorrespiratory support might be limited by hospital budget. Secondly, if & when nexts-of-kin argue this might not be in the best interest of patient or begin to wonder where this may lead, it could be a red flag to stop and wean support. In the third place, development of a serious complication (infection/ sepsis, hemorrhage local or elsewhere, CNS derangement) that may hamper recovery, should prompt the team to cancel support. And finally, it is up to the discretion of the responsible team to both, implement and disconnect support, according to own experience and on-site facilites.
I agree with abovementioned reasons: sepsis and irreversible neurological damage are serious indications. Timing of disconnecting ECMO is another issue. For this, discussing the matter with close relatives could play a major role.