Well, first of all, once the signal level recedes down into the noise level, it is going to be difficult to use the station's programming.
2nd, there are some better quality general coverage receivers that can do a darned good job of making a station very clear long after the typical car radio has given up the ghost.
You will find these at ham radio stores and on eBay once you know what model to start looking for. You will need an outside antenna wire, the longer the better but the length is not critical IF used only for Receiving...
What you want is a receiver that has DSP (digital signal processing), variable bandpass filtering at both the IF and RF levels.
Start reading up on Icom, and Yaesu ham radio products.
Uh, just one thing..... forget about getting one for $50 bucks.... get your wallet out.
$200 and up is about right for the quality that you are needing.
here are the factory websites.
Welcome to Yaesu.com
Receiver Products - Icom America
http://www.icomamerica.com/en/downlo...x?Category=132
Kenwood Radio used to make some good general coverage receivers, but their website tonight makes it appear they have abandoned that arena.
This is the one I have. Note that it is a transmitter/receiver but it has a General Coverage receiver that goes down below the AM broadcast band. The price on this one has dropped down into the range I mention as it is about 10 years old. Still damn good though.
http://www.hampedia.net/icom/ic-706mkii.php
All ham receivers have manuals that can be downloaded. The link above here has a direct link for the manual for the IC-706 MKII