[universe]

Under my kitchen counter in the pull out shelf there is a small pile of powdery debris. I clean it up and in a few weeks it is back. This has been going on for years. Nothing is falling off sides of shelf and there are no openings to shelf.

[Unknown008]

Perhaps termites? These are really annoying pests and can mostly efficiently get rid of it by replacing the furniture

[amricca]

Is the shelf rubbing on the bottom of the countertop or the sides of the cabinet? Might be something like sawdust from that, there should be signs of it if you look around the area.

[WVHiflyer]

Check the 'dust' carefully to see if it contains any insect body pieces. That would be the case if it's ants (the 'dust' is called frass and is a result of 'housecleaning'). Check the shelf and above the 'dust' for small holes. This could indicate a wood burrowing insect like one of the many powderpost beetle species (for a link on them, see my answer to the question about something eating furniture posted this week).

Perhaps termites?? These are really annoying pests and can mostly efficiently get rid of it by replacing the furniture

There is no type of termite that can be gotten rid of by replacing the furniture, unless that's where the queen has taken up residence - and that's only for drywood termites.

[themouseman]

Take a sample into your local Orkin or Terminex office if your around Chicago or Indiana or Michigan Rose pest mgmt . If not try looking under a large magnifying glass.
look for insect pieces. Its common for carpenter ants to leave a saw dust like pile near a colony. Check with a moisture meter for value of 19% or greater moisture in wall behind cupboard. If identified as carpenter ant or other wood destroying insect call above companies for an inspection.

if you decide to choose another not listed above contact you state agriculture or environment office for licenced and approved companies dealing with wood destroying insects. Or look for a national pest mgmt association member.

if in doubt insist on a sample of intact insect from your home before any work is done and store frozen in a container for a period of not less then 2 years if reinfestation occurs and they fail to honour warranty/guaranty you can prove that they failed to eliminate original problem via insect dna

[Unknown008]

^^ My first supposition was that the queen was in that furniture. 'Cause if this was the first time that universe saw these debris, it is most likely that the queen has made its nest there... And, WVHiflyer, I'm most familiar with drywood termites that's why I said so, though I didn't know any other types of termites making their nests in wood...

[WVHiflyer]

Unknown - sorry to imply you didn't know what you were talking about. But I thought too many might have misinterpreted...