Help me diagnose my car's problem. Dying battery or something else?

Can you all help me attempt to diagnose what is gong on with my car? Before I describe the problem, it is at the mechanic, but due to them being busy they told me it might be a day or two before they will get to it, so no need to worry that I will hurt myself attempting a home repair.

Here is the issue. First, the car is 3 years old, and is a push button start car. Two days ago when I tried to start the car it made a clicking noise and wouldn’t start. The radio, lights, etc. still worked. None the less, since I assumed it was the battery I jump started it and took it to the dealership. The problem was reported to be “a grounding cable that was throwing out a lot of resistance” and that was reportedly replaced. At the time they said the battery was good to go. Yesterday I had no problems, but today the same problem returned, just not as bed. It still clicks and won’t start when I try to start it, but every once in a while it will turn on. Since I didn’t want to mess with it any further at that point I took it back in to be serviced. It seems strange to me that a battery would work sometimes but not others, but maybe this happens with a dying but not yet dead battery? What do you car savvy dopers think might be going on?

I’m not a car savvy Doper, but I suspect that knowing the make, model, and year of your car (which you didn’t include in your OP) may be helpful to those who are.

Could be your battery needs charged? You can take it to a place like Advance Auto Parts and they’ll test your batter for free. They should be able to tell you if the battery is good, but just maybe needs a trickle charge or something.

I experienced something similar recently with my wife’s minivan. It’s got a lot of nice functions that are totally battery operated when the car’s not running (automatic doors, hatch, etc). I think these drain the charge quicker than your typical battery.

A bad ground can cause really odd issues. Here’s a good picture of one. They look attached, they may be physically connected, but just touching them can break them (like in the picture).

It could simply be a bad ground strap that was still making just enough contact when it started, but not enough, or none, the other times.

The only part about that that bugs me is that the dealership should have, or did, replace it. In that case, I’d suggest there’s more than one and/or they didn’t replace the one causing the actual problem.
For example, if there’s a strap from the frame to the engine and one from the body to the frame, it’s possible they replaced one (that may have been bad) and did replace the other that was actually causing the problem.

It could be a dying battery, it could even be a bad alternator (depending on how far you drove), but you said they tested the battery, so I’m guessing it’s neither of those.

ETA, and to add on to what Barkin’ said, it could also be a parasitic draw, but those typically take hours or a day to run your battery down. At least with that the test to see if it’s the case (not to find it though) is very easy and quick.