I'm seeing this sort of thing on my MI2S as well. It's currently running MIUI 5 v 3.11.15 from here but I've noticed problems in previous versions.
I've done some testing and I think that mobile data access is interrupting GPS somehow. I initially noticed the problem using navigation apps, where it would report incorrect speeds or lose position.
I've since tested using MyTracks. Basically I turn on recording in Mytracks and obtain GPS lock. Then access something that will quickly use a fair bit of mobile data, while I'm moving. This causes the GPS to lose satellites and try to re-fix. The speed vs distance log will show travel at 0mph, even though distance has been covered. Performance mode makes the problem slightly less noticeable for navigation, as it seems to find satellites faster again after an interruption.
Mobile data access interrupting GPS seems to be repeatable and more likely to occur when data intensive apps are running. Possible workarounds ar to disable Google location services or enable airplane mode to minimise data traffic.
Performance mode seems to help finding satellites again faster, minimising the effect of the problem during navigation.
I really hope this is a software problem and not a hardware issue. HTC One X users have had similar complaints and that sometimes turned out to be lose antenna connections (GPS or other radio antennae) inside the phone, requiring repair in many cases.