How do I fix squishy tiles in shower floor?
Even the best  re-grout jobs will fail if the sub-floor under the tile is compromised in some way. If the tile are installed on a damaged or wet sub-floor they will eventually loosen from the thin-set that bonds them to the floor. Over time this will be evidenced by cracks in the grout joints.  Before you try another grouting remove some of the loosest tile. Observe the thin-set below. It should appear solid with no cracks. Tap it with a handle of a screwdriver. It should sound solid not hollow.  If the tile removes with thin-set attached you will probably need to replace the entire floor. This is the time to ensure that the sub-floor and floor joists haven't been affected by water leaking through the tile.   If the showers' tile floor does need to be removed the standard procedure entails also removing about 12-14 inches of the lower wall so that a protective membrane can be installed. If you are comfortable with tiling, masonry, and carpentry this is well within a DIY-ers capabilities and can save a lot of money.