The same thing happens with my R9 270s, and the issue seems to be some kind of driver hiccup.  For me, the solution is to enter any arbitrary different intensity value (the point is to give things a jolt; the exact number doesn't matter), restart exeminer, then shutdown, re-enter the "proper" intensity value, and start again.  One of two things happens: either it just works after the restart, or it crashes the AMD drivers and then works perfectly once they recover.  For me the problem is worse if I specify multiple -I values with commas, vs. a single value for all cards.

Not a 6870, but on a 5870 TC 6144 -g 1 -I 18 and some minor OCing got ~190ish KH/s.