Shatterpoints speculation.

A paradox on its own is an engine that creates new timelines in a linear fashion: timeline A1 begets timeline B1, which begets A2 which begets B2, and so on. You can actually plot the growth of the paradox in metatime if you're so inclined. If the paradox timelines become a problem for Gaia, it can resolve the paradox in the latest timeline, preventing the system from creating new timelines. If needed, it can merge some of the previous ones together. Note that not every "classic" paradox becomes a paradox as we mean it, and plenty of things that don't look like a paradox satisfy this definition.

For example, let's say that Bob in some timeline A1 (we'll denote him A1!Bob) sends a message to himself in the past, creating another timeline, B1. In B1, Alice, motivated by Bob's change - and that's important - sends a message to herself, creating A2. If Alice's change undoes Bob's, then his original motive applies, and A2!Bob messages himself, creating B2... leading to B2!Alice creating A3, A3!Bob creating B3, etc., etc.

So, metafast forward to A413 or something. Gaia decides this has gotten quite silly and kills off A413!Bob before he messages himself. This prevents B413 ever coming into existence, and the system stops growing. It probably also merges some timelines - assuming no additional time travel, all the B timelines are easy to merge, as are all the A timelines except A413. The paradoxical system has been resolved with only two additional timelines created. (If it really wants to, it can then kill off the Bob in the merged A timeline, then merge it with A413, leaving only the A merger and the B merger. How difficult those are to merge depends on what the messages are, but the net result is still no worse than a simple fork - Gaia has bigger fish to fry.)

Shatterpoints start happening when you double up the paradoxes. This is where notation gets tricky. Instead of replacing letters, we're going to start adding letters. So we start with timeline A; A!Bob sends his message, creating AB; AB!Alice sends her message, creating ABA; ABA!Bob creates ABAB, etc., etc.

Now, we add a second pair of individuals, who I'll call Charlie and Diana. Charlie messages himself in response to Bob's response to Bob's message, and Diana messages herself to undo Charlie's message, just like Alice. In timeline A, there's nothing for Charlie to respond to, so A only creates AB. However, AB creates both ABA and ABC. ABC in turn creates ABCD. But in ABCD, Charlie never received a message for himself, so the conditions are right for him to create ABCDC, leading to ABCDCD, ABCDCDC, etc., etc.

Meanwhile, ABA's still around, leading to ABAB. ABAB creates ABABA and ABABC. ABABC creates ABABCD, which creates ABABCDC, etc. ABABA creates ABABAB, which creates ABABABC, which creates ABABABCD, which creates ABABABCDC, etc. You get it? It's not just linear growth any more - the rate of growth is itself growing.

But it's even worse than that. Diana's message undoes Charlie's, right? So ABCD is in the same state as AB. Meaning... ABCD also creates ABCDA. Which creates ABCDAB, ABCDABA, etc., etc. And, you guessed it, ABCDAB creates ABCDABC.

In conclusion, a paradox, or other infinite timeline engine, is fine. A paradoxical system with only one paradox grows at a constant rate, and Gaia can stop it by intervening in one timeline. But once you start mixing paradoxes, each timeline becomes responsible for own paradoxical system, which exhibits the same property. The rate of growth compounds, and the multiverse gets cancer.