Is it normal to love our dog less and less with each day that passes?

You need to show her that you are the pack leader.

Generally it's the owners fault for the dogs bad behavior. I've owned 3, all raised and trained well, very loving dogs. Most people are too stoopid and lazy to own dogs. They should instead bring a fire ant farm into their home. Fire ants make wonderful house pets :)

No. You never "throw in the towel". That makes you just as bad as the person who dumped her there.
What you need to do is get some books on dog training and watch some Cesar Milan. I have a Rottweiler Husky mix that didn't come from a shelter or rescue, but because her previous owners never trained her she was almost feral. Not in a fear based sense, since most actual ferals are scared of people, but in the sense that she was wild, disobedient, and hard to train.

She has bit me multiple times and escaped the fence a lot, but I've never given up on her. Now we've sectioned off the back yard with 6 ft fencing and she doesn't bite as much anymore due to training with a shock collar. I've only had to shock her a few times and now she only bites me if she's being moody because of her heat cycle or if she's gotten out and is afraid I'm mad at her. And it never happens except in a situation were she's cornered, such as showing her belly or wedged under the bed. Still not acceptable, but I just scold her then and try to tempt her out with a toy or walk. I never punish her for an emotional or fear based reaction. Just if she's being disrespectful or trying to dominate.

It may be a lot of work to correct and train your dog, but that's your duty. If she keeps getting sent back to the shelter she might be euthanized.
If you wanted an easy even tempered dog with no issues, you should have gone to a breeder. There are great shelter dogs, but they do often come with physical or behavioral issues. That's why if I ever get a dog again it's coming from a breeder. I will never give up on any dogs I own, but I will be much more selective in the future.

Well you never "throw in the towel" for starters.

I doubt you know how to train dogs very well because if you did you wouldn't ever say that.

Definately sign up for obedience classes as they are more about training you than the dog. It's also a bonding experience for the two of you.

As another poster suggested you have to be the alpha of the house. Start by keeping your dog on a very strict schedule as dogs are creatures of habit.

1. Have a regular food schedule for it to eat and don't deviate from it by more than 5 minutes. I do 8am breakfast and 6pm dinner.

2. Go to sleep at the same time each day and wake up at the same time. In the morning make sure you go about your business for at least 20 minutes after the initial greeting, them take it outside to relieve itself.

3. While feeding make the dog wait to start eating until you say ok. Make it sit before placing the bowl on the floor and do not allow it to eat immediately.

4. Have a daily routine for exercise. A walk or play time at the same time each day.

These are just basics. Since this dog is a rescue it has no sense of normalcy so it's extremely important for it to know it's needs will always be met. This is why not deviating from a schedule is important. Your dog will follow your schedule so do something thats easy for you to follow.

Remember, always give it lots of love. Also if it starts to bully, immediately isolate it for 5 minutes with a stearn warning. After 5 minutes show it love then forget the behavior.

I could go on for hours but you get the idea where to start.

This dog is showing aggression because it's confused. Teach it not to be. Best of luck.