When the timecop wants to return to the future, he presses a recall device, and in seconds he vanishes from the past and returns to the launch pad from which he departed.
We must be twice fair. First, we looked at such recall devices in analyzing Timeline, and found limited possibilities and serious problems with the concept that pushing a button in the past will return you to the future. Second, though, Timecop did it first; Timeline is the copy. Not that it matters; the problems are the same.
In essence, the core of the problem is that the recall device is not itself a time machine, and has no ability to send someone to the future; therefore for the time traveler to travel to the future, the recall device must be sending a signal to the future to tell the time machine to retrieve the traveler. Yet that future does not yet exist; that is, when the time traveler presses the button on the recall device he alters history--he was not there in the previous history to push that button--and before that signal can be received in the future, all of the events subsequent to the pressing of the button must unfold to create the history that leads to that moment (including that the time traveler must have been sent to the past). Meanwhile, while the signal is traveling to the future, the time traveler is stuck in the past up to the minute the signal is received in the future. With Timeline, that amounted to centuries; here the time is usually considerably shorter, a few decades, and short enough that the time traveler will have to make an effort not to interfere with the life of his temporal duplicate.
Eventually the recall signal reaches the future, the time machine activates, and the traveler is pulled out of the moment he pushed the button and deposited in the future, unaware that he was ever stranded in the past--unless somehow his actions prevent the time machine from existing in this world, or himself from being a time traveler. Agents should be trained for this, but they probably will not be, because no one will ever know that this happens. Either history will be altered such that the agent is snatched from the past at the expected moment, erasing all knowledge that he had ever been stranded, or the agent will never make his trip to the past, creating an infinity loop such that time is forever alternating between the version in which the time traveler is stranded in the past and that in which he never arrives.
Is there a solution?
Barring the possibility that the recall device is itself a time machine, there might in this case be one chance. Let us suppose that at the future end the time machine simultaneously transports the traveler to the past and returns him to the present. After all, at the instant the time traveler arrives in the past, from the perspective of the future end all of history is altered to whatever it is that he creates, including the moment he activates his recall device. It might be possible for the time machine to find the moment the time traveler hits the recall device as it is dropping the time traveler into the past, and pull him back as part of the same event. While this notion has some appeal, it fails: the time machine that returns the time traveler to the future is not the same one that delivered him to the past, because it is the one that exists in the new history, the old one having been erased. We hope that the machine is identical, but we already know that history will have changed the moment the traveler reaches the past, and this machine will be a temporal duplicate of the one that sent him. Besides, for the signal sent from the past to reach the future, the history from the moment it is sent to the moment it is received must be written--it might be that the time machine has ceased to exist in this timeline.
T.E.C. agents could, of course, return at the instant they left (perfectly reasonable--no reason for the the time they spend in the past to use time in the future), but this does not resolve the stranding problem created by the recall device. The only way around this is for the recall device itself to be a time machine.