I am using a Neewer TT520 flash with a Nikon D7000. I am new to flash photography. When I mount it on camera I noticed that at times the flash didn't fire. I've spent some time researching it and discovered that the red light takes long to turn back on after every shot. This wasn't the case initially (about a month back). Is this issue related to the battery or has it something to do with the camera settings?
The recharge time is shorter if your batteries are fresh. It is also shorter if you use more expensive ones , like Duracell than cheap noname brands from discount stores, like "Ikea" and "Powercell". Actually, some devices refuse to run on cheap batteries.
To improve the charge time further, use 1900-2300mAh rechargables. They have higher peak amperes and last longer. I recharge once per month, while normal AA batteries go flat after one session. You can get some that keep charged when not used as well. Example figure from http://speedlights.net/wordpress/wp-content/uploads/2010/06/yn460-ii_recycle_times_full_power_in_seconds.jpg
The fastest recharge I've ever done was when I rigged a flash to run off a car battery. It is not that portable, but for outdoor tripod work it is useful. You can also rig it to run from a PSU if you are near a powersocket.
You also gain recycle speed as you lower the power output, at a very good exchange rate. Two flashes of half power is the same light output but the recharge time for two half power flashes is faster than one full power. In my distant past testing, I lowered the recharge time to 25% as the power output was 50%.
Flashes are the biggest strain on batteries in photography, they use an awful lot of grunt. So I can pretty much guarantee your problem is flat batteries.
Manufacturers continue to use AA's because of their ubiquity; you can get them everywhere and pretty much any time even in remote locations. Because they're being pushed hard it does mean they will run down and go flat quickly.
You don't have to use rechargables but if you don't make the investment in a good charger and batteries you'll want to start buying good quality normal batteries in bulk/wholesale and don't bother with cheap ones, you'll end up with pockets full of 'dead' ones.
An additional factor in favour of NiMH rechargables (including the eneloop)is that they supply a good amount of power until they're practically exhausted which keeps recycle times good for a longer period. Normal lead-acid batteries ramp down their output more smoothly and the recycle time increases with each charge of the flash.