Is the loss of faith considered to have occurred if one commits a sin after having bound the existence of faith to abstaining from that sin for a certain period, knowing that the intention was not to swear an oath but to emphasize the matter?

The question is unclear. We will assume the questioner meant, "If I do not stop committing sins, I will not be a believer." This falls under the category of swearing by disbelief to do something. One should repent to Allah. If the action occurs, disbelief is not decreed. It is safer to offer an expiation for an oath.