Ah ha!
I'm also having this problem - the map goes blank and the app slows down, eventually crashes or stops responding...
I'm using it for mtb trail navigation.
The problem only really occurs on the trail - road seems mostly ok.
I think the cause is maybe the trail is rough, the phone shakes a lot and thinks its being reoriented (portrait to landscape and back) all the time rapidly.
This then causes osmand to throw a wobbly as it tries to re-display the map! Maybe?! Perhaps?! What do other people think?
I can set osmand to a single orientation in its options, and the phone also...
I'm pretty sure I tried osmand with fixed orientation though with the same problem..
Samsung S3..