The Static routing with Catalyst 3750 post has generated a lot of good, creative ideas. Some of the proposed solutions were better than the others and some were simply not implementable (but nonetheless, had great creative potential :). Here is my list of the favorites:
A routing protocol: as a few of you have rightly pointed out, this is the best choice.
Aggressive Unidirectional Link Detection (UDLD): this is my second favorite, as it's a reliable link-level mechanism that will detect a break in the fiber cable … exactly the right tool for the job.
Object tracking and reliable static routes would also work. This was my initial solution, but I was worried about its support in Catalyst IOS images. In the meantime, one of the readers has noted that the reliable static routing (or at least the configuration command) works in IOS release 12.2(37)SE, so this might be a viable solution.
GRE tunneling with GRE keepalives probably has performance issues (I am not sure GRE is ASIC-switched on Catalyst 3750). The idea is to create a GRE tunnel between IP addresses on the primary fiber link. If the connectivity breaks, but the subnet remains available, the GRE keepalives will detect the failure.
Spanning tree will not work. It does not test the two-way connectivity and might actually create a loop (if I stop receiving spanning tree hellos, I might assume the link is connected to a workstation and OK to use).
Etherchannel and LACP would most likely fail. If the radio adapters work as switches, so you cannot establish an Etherchannel across the two links. I am also not sure that the PAgP or LACP would detect a unidirectional link when the carrier is present on both ends. Any experience?
Bidirectional Forwarding Detection (BFD) is not available on Catalyst 3750 at all (the ISR routers got it as late as IOS release 12.4(15)T). Furthermore, BFD (as implemented in IOS today) detects a routing protocol neighbor failure, not an IP next-hop failure, so you need to run a routing protocol first (in which case we wouldn't be discussing this scenario, as we would have changed the boss, as someone has suggested).
Edited on September 9th to clearly indicate what would or would not work