Here are some rules that we've found to be true ourselves through frustratingly tedious trial and error:

-Make sure you always have a repel in use. If you encounter any random battles, it will break your chain, even if it's the same type of Pokemon you've been trying to chain.

-Always choose the same type of grass patch throughout your chain. If you started with a flashing patch, continue to choose flashing patches.

-Only choose a patch if you saw all four patches of grass shake. The reason for this is that there may be a patch that shook off-screen that you didn't see, and so the patch that looks like it's farthest from you really isn't. In our experience, whenever our chain broke, it was usually because of not following this rule. Along the same lines, it's a good idea not to step into the patch of grass directly behind your character, because it's often hard to tell whether or not it shook.

-Avoid the edges of the grassy area at all costs! Never choose a grassy patch that appears on the edge of the grassy area (make sure the patch you choose is completely surrounded by other grass patches on all sides). You should never even walk into the grass around the edges, or you may notice your chain disappear from the bottom screen on your Poketch app. Very frustrating! Try to stay as close to the center of the grassy area at all times to avoid this.

-Like Dawn/Lucas said, always choose the patch of grass farthest from you, but only if it also meets all of the other qualifications, like not being near an edge. If the farthest patch away from you is not the right type of shaking grass, you'll need to reset the Radar and try again.

Above: You'll need to reset the Poke Radar. A lot.

-Resetting the Poke Radar: if none of the grass patches meet all of the requirements, you'll need to reset the Poke Radar. To do this, all you have to do is walk the amount of steps it tells you to when you try to use it. This can be tricky though, because it's absolutely crucial that you don't accidentally walk into any of the patches that shook when you used the Radar last. Be very careful! If you can't remember exactly where all of the patches shook, just walk back and forth until you're able to use the Radar again.

-Pay attention! If you look away from the screen or get distracted for even one second you may miss seeing which patches of grass shook. Then you have to leave it to chance when you make your next move that you're not walking into one of the patches that shook.

-Never ride your bike or leave the grassy area. If the grassy area you're chaining in is very large, don't go so far that all the patches of grass that shook go off the screen.

-By all means, take breaks whenever you need to, because it could take hours before you find a Shiny. Make sure your DS is charged enough and either leave it open or close it to put it in sleep mode. You can save your game whenever you'd like, but turning it off will erase your chain. We recommend taking breaks during battles or right before you reset the Poke Radar, so you don't forget where the shaking grass patches were and accidentally walk into one.

-Above all else, BE CHOOSY. If none of the shaking patches meet ALL of the above requirements, reset the Radar and try again! There is a high chance your chain will break if you don't follow all of these rules every time you try to build the next link in your chain. Because of this, you will probably be resetting the Poke Radar a lot more than you'll be choosing grass patches. Be patient and you will avoid the frustration of having your chain break, especially when you've already put lots of hard work into building a big chain.