Busy beaver candidate elimination: Minimum space requirements
There are many methods for detecting that specific TMs will run infinitely. As Marzio mentioned, Heiner Marzen's page and papers provide almost all of the currently used methods.

The method you describe is a great simple requirement. Specifically, if we know that the TM has only moved around on a small tape of size $N_{tape}$, then the exact configuration at every step so far can be described by (1) the symbols at each of these $N_{tape}$ cells, (2) the position of the reading head and (3) the TM state. Thus there are $|Q| \cdot N_{tape} \cdot |S|^{N_{tape}}$ possible configurations (Where $|Q|$ is the number of states and $|S|$ is the number of symbols). So, if the TM has taken more than that many steps of computation, you know that it must have been in one configuration at least twice and thus that it will infinitely repeat.

However, I don't think this method works very often in practice because it is more common for TMs to run off infinitely in one direction than to stay on a small section of tape.