Why is grout at tub edge disintegrating?

1. Too big of a gap between the tub and the tile.
2. Using grout at that interface.

The tub, sitting on the floor, is going to move relative to the tile (attached to the wall), especially when water is added to the tub. Whatever is used to seal that area needs be an elastomer, like GE Silicone II (just one of many products available). But they are limited in how wide a gap they can seal.

Here's picture of my tub/tile interface before it was caulked. Gap is 1/6" to 1/8" all the way around.

I've seen similar gaps in caulk around tubs. It may not be the same as your tub, but it was caused by the floor shifting from water damaged joists.

It could also be the quality of the caulk and/or how it was applied. If it was applied unevenly without fully filling the gap the thinner area can shrink and open up. This is also due to low cost/quality caulking.

Other possibilities are there was soap film on the surface that didn't allow the silicone to adhere, the caulk hadn't cured fully before it was subject to water, and the gap was to wide for the caulk to fll in one pass.

The repair is to cut out the old dried caulk being careful not to cut any deeper than needed (there may be felt membrane behind the tile). Vacuum out the loose pieces. Lay down some blue tape for a boarder and re-apply 100% silicone. Allow to dry for the prescribed length of time (12 hours).

That is not grout in that section.

That is either caulk with grout layered on top of it

or

Caulk that looks like grout.

Grout does not curl when it is installed incorrectly, it cracks and breaks off in chunks.

You can caulk over grout at tub top but cannot grout over caulk (and caulk that looks like grout is usually crap).

Since the gaps are on the larger side - not obscene but larger - I would try to grout the area... see if it lasts without cracking and then silicone over it if you notice it cracking.

If you try to apply silicone you will need to go deep into cracks (1/4-1/2"), get an edge, let it dry and do another round or two of caulking. You cannot do all of that silicone at once or when it cures and you have a failure piece, the whole system will come out in chunks of silicone.

So here it is - The yellow highlight... that's grout. The red circle is an example of an area (not the only area) that is not grout. The webbing at the top of the "grout" shows it is not grout as grout doesn't do that, ever. You see how dry the yellow area is, that is what grout looks like. Grout cracks in large lines/chunks.

Also if there is caulk on grout - what some are suggesting and maybe...

1. Wow when you grout you fill the damn gap if this is the case I am not even sure if they filled half the gap.
2. The caulk wasn't silicone (should be) - silicone doesn't dry or peel like that. Sure looks like caulk that looks like grout.