It sounds like you have cutworms and the moles are digging to get them. Moles usually stick around if there are grubs to feed on and disappear when there is nothing to eat.

Cutworms cut off the plant to trap the nutrients in the roots and then they feed on them. Dig under a cut off plant and you will find a gray or white curled up grub. Unless there is a bug infestation there is usually only 1 for each plant that is cut off. You can buy grub or cutworm killer but if there are only a few digging out the grub and killing it is the easiest and best way.

Thanks for the information oilpainter. My dad had the
same idea, so we must be on the right track.

Another note in the continuing saga of impatiens....I've just been digging some of the remaining healthy plants up to salvage them, and I'm not finding any bugs of any kind. Earlier, when I first noticed the moles, I sprayed the whole flower bed with Bayer complete insect killer. What I am noticing is that the flowers that seem to be sheared off have a spot right at the base of the roots that has a black, slimy area completely surrounding the stem of the plant. Even some seemingly healthy plants have this black area, and if you touch the plant there it will fall over, just like it was in the ground. So now, I'm wondering if it's some kind of reaction to the insect killer (which is supposed to be safe for plants) or maybe some kind of fungus. I'm getting pretty desperate here, since plants to replace the dead ones are getting really scarce in my area. Help please!!!

Oh, oh---you have root rot and there is no help for any plant that has it. It will be in the soil now and infect any plants that you put in there. You must have had very wet weather.

What I would do is treat the soil then cover it with black plastic, cover the plastic with mulch and plant in pots and set them on the mulch. Check out the site below.

http://www.oznet.k-state.edu/path-ext/factSheets/Ornamentals/Root%20Rot%20Diseases%20of%20Flowering%20Plants.asp

Root rot is cause by too much water and bad drainage. If you let the soil dry out more this should help. At least this helps for me. Damp off is the big worry this usually afflicts seedlings though. Earlier in the season we had a lot of rain and big fluctuations in the weather from hot to cold and some of my plants started to get root rot but I let the soil dry and most made it. If though your plants are mush they are goners but you may be able to make some cuttings.

I'd try the cuttings idea - i've been 'pinching and poking' and having great success this year b/c of the wet weather we've been having...