From my perspective, it goes to the character of the company. Perhaps they are inundated with applications, and simply cannot reply with "sorry but no" to everyone. Of course, another option is that they just don't care about your feelings, and if you are selected, so what.
In their defense as well, they probably have hired many part timers, only to have them quit after one day because the work is too hard, or they found a full time job. Many job-seekers don't consider the company's perspectives when quitting, and don't give notice, or give partial notice. Either way it is, the best thing to do is keeping applying to other companies. If you submit a resume for a job that you really want, and you don't get the call, try retooling your resume. Then when you see the same job announced again, you can resubmit your resume. I got one job that way. The guy they hired flamed out, and I got the call after I retooled my resume to be industry specific.
Hi Sajida: Jeff brings up some good points here. But I would also suggest getting in contact with UPS about your application - you don't have to wait to hear back from employers. Call the location you applied to and ask about your application. It could be the push they need to give you an interview!
You should always be, and stay consistent. Calling everyday increases your chance of receiving the position.