Keep in mind that once you get residue of rosin on your strings, they can be a bit sticky, especially if you play with a flatpick. Clean rosin residue off your strings with a soft cloth that's damp with a little rubbing alcohol. Avoid getting alcohol on your instrument's wood or on the fretboard.

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Demo of Hammered dulcimer with Jimbow

A dose of rosin should certainly last more than 8 measures, even on a Mountain Dulcimer!  Could be you're not dosing with enough rosin; or pressing down too hard are wearing it off too quick. 

Hammered Dulcimers are going to be nearly impossible to bow. 

Bows used on Bowed Psalteries certainly last for more than one song!

How long should the rosin work before you need to reapply. I am trying one out on a MT. dulcimer and the rosin wears off the bow & it wont sound after about 8 measures.

Any ideas?

Do they work better with H. dulcimers (the bow are a bit bigger)