Drying fruits with a household dehydrator
It is possible to dry fruit with a household machine.

How long it takes will depend on the relative humidity. When I lived in Texas, drying would take 24 hours- sometimes more. Now that I'm in a high altitude desert drying is sometimes done in less than 6 hours.

At very high humidity fruit may get moldy or just too oxidized before it is able to dry. A unit with a heater will help a lot with this. 
After the fruit is dried, keep it in an air tight container to keep it from absorbing water from the air and molding.

If you find your unit just isn't able to move enough air you can try Alton Brown's method and bungee cord an AC filter to a box fan and put it in your window. That will move a lot of air and dry things relatively quickly.

Keep in mind that home dried fruit can be dissimilar to purchased dried fruit. For example, apricots are treated with sulphur to preserve their orange color but it affects the flavor. Home dried apricots are darker and not as soft but have better flavor.

It's also possible that your bananas are too ripe.
Bananas are dried when they are only barely ripe- or slightly under ripe. Ripe bananas have so much sugar that they stay chewy and sticky for a long time. On the plus side they have a lot more flavor than commercial banana chips.
Recipes for banana chips will sometimes call for just ripe bananas and toss them in acid to keep them from browning.

If your bananas are still sticky they are definitely not done and will mold if you store them very long. Try giving it a good 24 hours. If that still isn't enough then either your machine isn't moving enough air or the air is too humid.