Monasteries in general did not have troops, as is witnessed by the fact that they were frequently invaded and destroyed by small groups of men who usually martyred a couple monks in the process. Indeed, I have not encountered any mention of armed forces garrisoning a monastery in the primary sources. I would be interested in seeing your source that says otherwise.

If we're talking about sixth-century female monasteries in Poiters, then we're usually talking about the monastery of the Holy Cross founded by Radegund, wife of Clotaire I, who was also the foundation's first abbess.

There are two general types of monastery which we find in the Merovingian period: those which were built in or near cities, and those which were built on the borders between diocese. The former was under the control of the local bishop and usually founded by him or with his encouragement, while the latter was situated in such a way that it would be very difficult of a bishop to assert his authority over the foundation. The latter type of monastery is usually also the type which was designed as a projection of power, but that projection was economic and legal, rather than military.

Radegund's monastery is located here and is certainly of the first type, built within the city. As a refuge rather than a projection of power, it is unlikely that the monastery itself would have anything more than a doorwarden. Despite being founded by a queen, the monastery would not have had much royal support. Radegund, after all, did not enter the monastery on the best of terms with her husband.