I used to do this a lot, especially when doing long cross country flights to controller airspace I am not familiar with. I stumbled on a rather dated product called BackTrack. This is a small box that was originally intended for folks to practice guitar riffs, etc. It has in and out standard headphone jacks, and records everything that comes over the input as a clip. For important clips, you can press a single button and "mark" that particular clip. You then have a playback button, and it simply plays back the last clip. You can also switch it so it only plays back the last marked clip. Ultimately, you end up with hundreds of clips for a given flight which you can copy to a computer and play back at any time.
It works VERY well for my purposes, and I only wish that Dynon offered such a capability. I have tried to design a similar product (to sell), but that is quite a challenge. In the mean time, BackTrack works great for me for those times where I feel a need to have the means to record all ATC conversations.