Presets load the entire set of blocks to the active memory. when you change presets, those blocks and memory are wiped and need to change to the next set. there has to be a brief break of audio as things are changing quickly.
there IS a Spillover option on all Axe-Fx products, which allows delay and reverb trails to continue when changing presets. you can turn it on. but what happens is the audio from Preset 1 that's repeating/trailing, is "given" to the new blocks in Preset 2. if you have the exact same delay block setup in Preset 1 vs Preset 2, it will sound the same as it trails (albeit with the slight needed gap when changing presets - almost all digital products have this gap given how digital products work). if the delay block in Preset 2 is setup differently, the trails will change sound to whatever Preset 2's delay block is - again, that's how digital works. if there is no delay block in Preset 2, there will be no trails because there is nothing to play the trails through.
what many people want and the way they think it works is that Preset 1 delay is trailing, when you change presets that trail should just continue until it's done. well again, what "block" is it trailing through? it has to be something. in order for P1 Delay to keep going when you change to P2 with no delay block, that P1 delay block needs to continue to exist somehow. the memory has to be there. for this to happen, there would need to be 2 Presets active at the same time: Preset 1 active while the trails fade, and Preset 2 when you change so you can immediately play those new sounds. but really no digital processor is designed to have 2 presets run at the same time. and then the question is when exactly is the first delay "done"? when we can no longer hear it? the unit would have to be designed to monitor the signal going through that first preset until it's "done" making a delay sound. this all gets very complicated.
to us humans with a brain and logic, it's clear when a delay would be "done" making the repeats. but to a machine, it doesn't "know" when we're done with that delay.
the way the Axe3 deals with this is its expanded Layout Grid capability and increased CPU power, as well as Scenes. again, a Preset loads all blocks into active memory to be used. in the Preset we can bypass blocks all we want without issue because it's loaded into that active memory and we're basically muting and unmuting it - no memory needs to change. Scenes allow us to turn on/off multiple blocks at a time. so Scenes are the best way to get spillover while changing sounds. all blocks are loaded, no memory is changing, we're muting and unmuting blocks, and that is the "2 presets loaded at once" concept in action. the "presets" in this case are Scenes though, as all the blocks needed are active and loaded.
Scenes are the answer and the approach to solving this problem. you can also use the Spillover settings in Setup to have it between presets.