You need to pay significantly more than that.
Im also looking for one as well, because my current MP3 (Sony walkman A series, 50hrs of battery life) i bought about 4 years ago is starting to die out. [BTW this is not being produced anymore, so you wont be able to get it, unless you go for 2nd hand market]
The reason why your player dies out quickly, is (my speculation) because you put the sound on quite loud, don't you? In which case, even if you buy a new player costing $20-30, it would yield the same results.
If I were you, I would spend significantly more than that for an MP3 player. Its better to pay for a player that would last for a longer time (2yrs or more) than having to buy cheap ones every year or so.
Having said that, I would recommend SONY walkman series, iPod shuffle, or one of the COWON series [ although im not too sure about their products, but seems to get good reviews on it] for cost-battery performance.