The 6th entry for away in MacMillan:
[usually progressive] used for showing that someone does something continuously or for a long time
Molly was at her desk working away as usual.
The children were all chattering away happily.
I think this definition is a restricted usage of away, and it has to collocate with a dynamic verb.
However, not all dynamic verbs can work in this way:
laugh away / jump away / hit away / dance away / ponder away / wave away / make away / push away / submit away / integrate away / explain away / warn away / protect away / help away / shoot away
I think verbs with the atelic aspect can always work with this definition of away, is it true? What about other aspects?