The fact that it will re-start shortly after it's been run suggests the alternator is charging. The important point here is whether something is draining the battery whilst the engine is off (which could be a faulty alternator, or car alarm etc), or whether the battery itself is unable to hold a charge.
You need to measure the current drain with the ignition off, by putting an ammeter in series with one of the battery cables. Current drain should typically be under 20mA, and usually quite a bit less than this. A low value on this test points to a duff battery. If you get a high value you need to start disconnecting things (start with alternator) until you find the culprit.