I have had this plant for almost 3 years. Over this past winter the leaves are partly covered this a shiny, mildly sticky liquid. The plant, which has always been healthy looking now looks sick. I don’t see any insect on the plant, Any suggestions.
Palm is a generic term that is used to refer to many different plant species, some of which are not Palms at all. Without knowing just what plant species you have or a more specific description of the stickiness you mentioned, I can only make an educated guess as to what is happening. Good photos are always beneficial.
It is likely, that your plant has an infestation of scale insects. These insects don’t look like insects as we think of them. They are slightly raised bumps about the size of a small match head. When young they are translucent and hard to spot. When mature, they develop a hard, brown shell and stop moving. They suck on the plant tissue and secrete the sticky stuff called honeydew.
Close relatives of scale insects are mealybugs. They look like tiny flecks of white cotton and are more noticeable than the scale. Both are treated in the same manner.
Mix a solution of 5 parts water, 1 part isopropyl (rubbing) alcohol and a squirt of liquid dish soap. Spray this solution over the entire plant covering all leaf and stem surfaces until they are dripping wet. This is a messy job, but thoroughness of coverage is critical to eradicating the critters.
One other note: plants under stress for other reasons (over potting, and improper light or watering) are much more susceptible to pest infestations. Whenever there are pest problems, there are also usually other care issues. It is quite possible to eradicate the pests, but the plant continues to decline due to some other underlying care problem.