You have the problem of too much mass resulting in nuclear fusion starting up. This would be the lowest mass for red dwarfs under normal circumstances (or brown dwarfs who are past the deuterium burning stage). See the wikipedia definition for "brown dwarf". Brown dwarfs are typically from 5 to 90 M_jupiter but whether fusion takes place and how long it lasts will depend a lot on the composition.

Now you could get around this if you constructed the planet out of elements that are difficult to fuse, say carbon or silicon. Ultimately you could use iron which can't fuse at all (see wikipedia "Stellar Nucleosynthesis" or "Silicon burning process"). Using those elements you may be able to build a planet up to the Chandrasekhar Limit (~1.4 M_sun). Though I doubt anyone has looked at it I think you could go larger than that if you don't make the "planet" solid. I.e. build it so that the mass becomes increasingly distributed as the "planet" grows. In this way one may not end up with gravitational forces that overcome the electron degeneracy pressure. Of course this would not be a natural structure and would have to be "manufactured".

Good URL on stellar evolution:
http://www.astro.columbia.edu/~archung/labs/spring2002/lab03.html