I've had my 2003 dodge neon sxt for over a year now and about 6 to 8 months ago i've replace passenger side motor mount that is on top several times.
Why would it break so many times, what is wrong that it keeps on breaking?

 

Crappy design. I bought motor mount inserts to help keep them twisting, therefore keeping the mount from breaking. Those torque strut mounts are there to keep the engine from rocking back and forth, so they will eventually tear from the rocking motion. Inserts fill up the empty space in the mounts. Mine have been fine since I installed the inserts.

 

Here are some suggestions why your upper mount keeps failing. 1. The other mounts are shot too, and the excessive movement is tearing up the new mount you are installing. Check the lower torque strut, and I'll bet the right engine mount is broken. The right engine mount is the one that is between the upper and lower torque struts. The bolt that secures the mount to the engine is in the right wheel well under the plastic cap. 2. If the other mounts are in good shape (I doubt it), it could be a poor quality mount. I replaced my son's upper torque strut and the center was made of phenolic instead of aluminum; it lasted about 3 months. Avoid Checker engine mounts. You can get a very good price on the mounts from dodgepartsonline.net