I read your post to mean the military "client" is the owner of the home and he wants you to manage it for him. With that in mind, here goes.
A month-to-month lease means that you can give a 30-day notice an the tenants are supposed to move. The 30-days actually start on the first of the next month (for example, a notice given on the 10th of March means the tenant has until the end of April to get out). If they do not move then you have the time and expense of an eviction. If your military client has the ability to give you that much notice they are coming back and want to re-occupy their home, great. If not they would have to stay with family or friends or check into an extended stay hotel for a time until the home was ready for them. Not the end of the world but something to keep in mind.
As for finding short term tenants, Jon K is right that most people do not want to move that often and there are the turnover expenses but if you are managing, those expenses are passed on to the owner (military person in this case). I would still charge my normal fees for finding a tenant (1/2 month rent in my area) even if the tenant is only there 3-4 months. You are helping the owner cover their mortgage while they are deployed.
There is a good source of short term tenants to go after, however, depending on the size, condition and location of the rental. You have Corporate (local companies that fly in execs from other locations or countries for short term projects etc), Vacation (there are whole websites dedicated to vacation rentals and all of them are short term and usually at a higher daily or weekly rate than if you rented by the year), Insurance claims (a family needs a place to stay while their home is being repaired due to storm damage or some other disaster). In most of these cases you would have to provide a fully furnished (and in some cases include all utilities) unit including dishes, towels, TV and so on.
Where there is a will, there is a way. Good luck and hope this helps.