The Airave is only a 3g CDMA over Broadband solution. When you choose CDMA only it's the only choice and is a strong connection. With LTE enabled the device is still trying to keep an LTE link but since your coverage area sucks it keeps falling off. Seems the Sprint GS5 has that issue for everyone where there is bad LTE coverage. It may also be that "Connections Optimizer" crap.
I'd suggest tasker or a similar app for automating setting your mobile network to CDMA Only when at home or elsewhere LTE is crappy and creating another to revert back to LTE/CDMA. There a bunch of threads with people trying to figure out how to optimize their LTE band for their specific coverage. I burned a lot of battery with my N4 constantly trying to decide whether to stick with HSPA+ or other crappy alternative networks. I don't think Google or the manufacturers have done a good job of considering what happens under less than good conditions signal wise.
LG G3, GS5,
GS2, G Tab 3, G Tab 10.1, iPhone 5S, iPad Air, Kindle FireHD, Nexus One, Nexus 4, Nook, Palm Pre, Sensation