By skipping do you mean the audio cuts in an out or are there brief pauses in the music? If it's the former, the headphone jack may be breaking.
Yes, if the disturbance is a temporary 'zero volume' rather than a temporary 'pause', then it's most likely a faulty connection as stated. If the device is failing to decode correctly, it could be a number of things...
0. First try new headphones. Wiggle the connector to see if the plug/socket has bad connection. If it's a physical problem it requires a physical solution.
1. Failing that, if your mp3 encoding is too high quality, the device might not be able to cope. I would try normal 44kHz 128bit/s normal stereo CBR encoding.
2. The song may not be ripped correctly, if you ripped it yourself. (You should always enable 'syncronise the ripping' for high speed drives.) I'd test the skipping mp3s on my PC to see if they play right. But also, the default mp3 encoder you're using might not be standard, and might not be supported on the player. I suggest always using the LAME codecs for mp3s.
3. At one time, when downloading an mp3, the browser sometimes screwed up the file format causing a skip effect to be heard on playback. I don't think that this will be the problem unless you have an old PC / browser software.
4. Failing that it may be corrupt software, on your player. And if it were my player, failing the above, I would restore factory settings at this point.
5. Failing that I'd look on the net if others had problems with this player by searching the make/model and looking on the various forums.
6. If there's still no luck, I'd wonder if the factory settings may be damaged, so I'd download new firmware from manufacturers. (If possible to install new firmware)
7. Failing that it's probably an irreparable hardware fault, as a result of impact damage, or shoddy construction, and so I'd buy a new device. Depending how upset I was, considering whether I took good care of my player, and used it normally, I might avoid buying from that same manufacturer again.