This may technically be 2 issues, but I think they may both have a common cause. I am using the v0.6.0 release of mGBA, playing on a New 3DS XL with Luma3DS v8.1, and I have encountered this issue on both the CIA and 3DSX builds of mGBA. I have not encountered this problem with the PC versions of mGBA, but I have not done as much testing on those systems. I do not believe this is a regression introduced in v0.6.0, as I recall having this issue in version 0.5.2 as well.

First, I was playing Pokemon Prism, and at the start of the game I did my best to set the in-game clock to the same date/ time as my 3DS. However, after playing the game for a while, I saved the game (and also did a savestate) and closed mGBA, and when I reopened it and started playing the game again, I noticed that the in-game clock was behind my system time by roughly the amount of time I had stopped playing. However, I believe this is incorrect behavior, as the in-game clock should be kept in sync with the system time.

Furthermore, whenever I put the 3DS into sleep mode with the game open, the in-game time speeds up by a considerable amount. I started playing the game on Saturday July 22, and after leaving the system asleep for a day or two, my in-game clock said that the date was somewhere in the middle of October! And when I opened the game today, it now says it's December. Even if mGBA isn't supposed to manually change the RTC to the system time, I believe that the RTC still shouldn't run so fast when the system is in sleep mode.