As some of you have said, Alamo is about halfway between Jackson and Dyersburg. That alone would make it tough for an Alamo (only) station to survive. (BTW, it's Jackson, NOT Jacksonville. Leave Tennessee to the Tennesseans.)
The situation that you have there in Crockett County is very similar to what we have here in Cheatham County. We are a bedroom community to Nashville, and are situated between Nashville and Clarksville (for those of you on the north side of Cheatham County), or between Nashville and Dickson (those of us on the south side of the county). We recently lost our only AM station, WQSV in Ashland City, but it wasn't much of a loss. They totally ignored the south side of the county, and their signal was atrocious (at best) here. But at least WQSV, while they were on the air, attempted to make a real go of it. They were live in the morning, although (apparently) automated the rest of the day. Definitely no wall-to-wall NOAA radio was ever heard over WQSV.
We have one of the FISH frequencies with a COL of Kingston Springs, and the GAME (sports station) with a COL here in Pegram, but both of those are Nashville stations.
Dickson lost their AM station about four years ago, but returned a few months later with new owners, who eventually also acquired an FM translator for them as well. Apparently Dickson is just far enough away from Nashville that they can support their own station.