Tile Grout: Patch up gaps, or strip out grout and regrout the whole thing?

I have tiled walls around a built in enameled tub. The tile itself (4×4) is in excellent condition. However, there are a lot of gaps in the grout, from half an inch to two inches in length, scattered around.

The tile job was done about 16 years ago.

I like the tile and want to keep it. (It is pretty.)

Should I strip out all the grout and regrout the whole thing? Or is it OK to just push some grout into the gaps?

Thanks!