SAX J0635.2+0533 is a binary pulsar with a very short pulsation period (P=33.8ms) and a high long-term spin down (P>3.8x10–13s/s), which suggests a rotation-powered (instead of an accretion-powered) nature for this source. While it was discovered at a flux level around 10–11erg/cm2/s, between 2003 and 2004, this source was detected with XMM-Newton at an average flux of about 10–13erg/cm2/s; moreover, the flux varied by over one order of magnitude on timescales of a few days, sometimes decreasing to below 3x10–14erg/cm2/s. Since both the rotation-powered and the accretion-powered scenarios have difficulties to explain these properties, the nature of SAX J0635.2+0533 is still unclear. Here we report on our recent long-term monitoring campaign on SAX J0635.2+0533 carried out with Swift, and on a systematic reanalysis of all the RXTE observations performed between 1999 and 2001. We found that during this time interval, the source remained almost always active at a flux level above 10–12erg/cm2/s.