So the only place I could find this was on Amazon, with this description (bold emphasis mine)
This item YuanLey Gigabit PoE Injector 30W, PoE+ Injector Converts Non-PoE to PoE+, Power Over Ethernet Injector 48V IEEE 802.3at/af, 10/100/1000Mbps PoE Adapter Plug & Play, Distances Up to 325 Feet
WHile both POE_ and 802.3at are 30W, 802.3at is 54V, POE+ (pre-standard, mostly Cisco) is 48V, so this is NOT an 802.3at injector, this is a 48V POE+. This will not work on APs that require 802.3at at 54V to operate (like the AP-27x and all outdoor APs after that require 802.3at). So send this back and whatever you buy, make sure it's 54V 802.3at, NOT 48V :)
Additionally, it's worth noting that POE injectors are PASSIVE (a little known fact), so even if your switch is only 802.3af 15W, if the injector senses ANY POE power on the non-powered line, it will pass on whatever PoE it detects on to the powered port, and will not 'inject' it's own power (whatever it supports).
But I'm pretty sure the AP is not detecting the voltage it would expect 51V+ after the cabling drop, and is likely seeing 47 or less which the AP will not operate on.
Let us know if you find a true 54V AT injector and if it works!