Yes, definitely repot your palm. It may be that it has just become top heavy, or it may be root bound. Don't use too large a pot, though. Go up just one size, unless your palm is very large, in which case you might be able to get away with a pot 2 sizes larger.
I have moved my tree into a pot one size larger and added the cactus soil to the pot. I am worried that it may be something like root rot. The new pot and soil should drain very well and I am going to move it to a spot that gets some more sunlight. If it is a type of root rot, can it recover from it? When I transplanted the tree I noticed that the base of the tree has a small "crack" in it.
When I was posting, I thought to myself that root bound plants are usually tight in their pots, but my brain didn't make the connection with my fingertips, so my thought just fell by the wayside!
It happens to all of us sometimes
It should recover if cared for right. When you repotted it, did you notice if the roots were strong with white tips or brownish and frail? Frail roots are a sign of root rot. The best thing to do if the roots are rotten is to treat it with a fungicide and plant it into an inorganic soil (like lava rocks) until you feel it has taken root.