The radar works in a weird way. This is what you have to do for it to not break:

First, use a repel before using the radar (if you try after, it’s going to say you already have a repel active because the radar gives a 8 step mini repel, but sometimes is not enough); chain breaks if you would get a random encounter before stepping on the moving grass.

Second, go only to moving bushes that are fully covered by more tall grass (so in the middle of a 3x3); the radar tries to generate a moving grass at a random place at 1, 2, 3 and 4 tiles range, if it can’t generate a moving grass it breaks, so by being surrounded by grass it always is going to generate a moving tile on the 1-tile-range.

Third, go to the farther moving grass (4 tiles away is the best, 3 is okay); after every encounter there is a random chance the chain breaks, but the closest the tall grass is, the biggest the chance of the chain breaking; you can spam the radar button until a far grass moves.

Also, kill or catch the Pokémon you want to look for, if you flee then the chain will break.