Things in orbit don't de-orbit because of gravity; in fact, gravity is half the reason things are IN orbit (the other half being the fact that they're going really really fast).
In ideal conditions, your ship's orbit would never change. There are two non-ideal things which will change the orbit over time:
Non-spherical earth: this will cause the orbital parameters to change, though I have been unable to find a good source of the math to tell me how. AFAIK though these effects are relatively minor.
Atmospheric drag (yes, there's atmosphere still up there): half the reason things are in orbit (and part of the definition of their orbit) is their speed. Drag will slow them down, thereby changing their orbit. Drag is effectively the same as a light retrograde burn, and retrograde burns is one of the most effective ways to lower your orbit - so effectively you're continuously lowering your orbit. How long it takes for this to effectively de-orbit your barge depends on a lot of factors, including how aerodynamic the ship is.
I found one interesting site:
12). How long will orbital debris remain in Earth orbit? The higher the altitude, the longer the orbital debris will typically remain in Earth orbit. Debris left in orbits below 600 km normally fall back to Earth within several years. At altitudes of 800 km, the time for orbital decay is often measured in decades. Above 1,000 km, orbital debris will normally continue circling the Earth for a century or more.
So, without orbit maintenance, it would be reasonable to assume a few years before decay.
However, interstellar spacecraft must have mastered the ability to transfer energy with them efficiently for space travel (i.e. they'd never work with today's rocket technology) so engine power is effectively a non-issue in planetary orbit. Also, if the ship is not designed for re-entry, then it must have craft that is - presumably also with the same level of engine efficiency. A ship like this might instead be in geosynchronous orbit instead of LEO because it can be very beneficial to continue seeing the part of the world you cared about to begin with (or to continue being in contact with the landing craft you sent down). The primary reason things nowadays are in LEO is because it would just too uneconomical with our current rocket technology to not do so.