Running a Radio Transmission System

With a scanner you'd be looking for a change rather than a fade, but you probably meant that.
A directional antenna might fix the issue, however you might also make it worse, the problem is very difficult to diagnose by proxy, however elevation sounds like it might be an issue for you.
If you can get a directional ant cheaply might be worth a try, however what you really need is someone with technical knowledge of Rf there to weigh things up.

Is there a TV station near by?

there is software for doing link analysis. i have a very old version of **broken link removed** that has no restrictions on the system frequency. i think the newer version i linked to may be limited to amateur radio bands, but not 100% sure of that. the software uses GIS topographical data, variables such as antenna height and antenna pattern, and draws a coverage map. you can add network nodes and see the usability of each link.

SamTaylor said:

With the problem sites there isn't a great line of sight to the base station. Both problem sites are in a constrained valley (+-50m below the elevation of surrounding ground) and there are quite a few big buildings in the way. Would this create problems for a yagi?

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No, quite the opposite - it's where you USE yagis - the difference between an omnidirectional (minus gain) and a yagi is absolutely huge. I suggested 10dB previously (for a ten element one), but that's 10dB over a dipole, so it's likely to be even more over an omnidirectional aerial (unless it's actually a vertically polarised dipole).