Download a copy of the 1991 service manual (since your car appears to be a coupe, not a T roof). You can find links to free .pdf copies of the SM in the Prime Wiki. On pages 20-56 and 20-57 you will find a rather limited description of the hatch release mechanism.
Is the latch release lever free to return to its normal vertical position? In particular, can the lever swing back and forth through its typical 90 degree movement with no feeling of a spring wanting to return it to the normal straight down position? If so, chances are that the return spring in the latch assembly has failed. In order to check this you will have to remove the latch assembly and inspect it. The latch is fairly easy to access and as I recall is only retained by two bolts. Given the age of these cars, the failure of the latch return spring is almost certainly age related. However, if the latch is particularly grotty cleaning and lubricating might fix it.
If the release lever has a fair amount of free movement with nothing happening at the latch end , the problem may be the cable retainer or the adjuster. If you look on page 20-56 of the SM, you will see a picture (in a circle) of the mechanism that Honda uses to adjust the slack in the cable. If its like the door release cables the cable end fitting has three grooves in it and you fit the groove in the cable into a retainer selecting the groove that gives you the correct cable slack. The grooved end fitting is plastic and the ribs between the grooves may have snapped or deformed allowing the cable end to slide back and forth in the retainer clip. Unfortunately, this adjustment is at the release end of the cable so its a lot of hassle to inspect. The other possibility is that at the latch end of the cable in the engine compartment, the cable is retained by a clip on the latch assembly. With an inspection mirror and a flashlight you can see the end of the cable and its attachment point. If the retaining clip deforms it looks like the cable outer jacket could slip through the retainer creating a lot of lost movement.
I would definitely start by inspecting the latch assembly, either for return spring failure or movement of the cable housing in its retainer. Even if you have to unbolt the latch to check it this will be much, much easier than accessing the end of the cable at the release lever. With the latch assembly unbolted; but, still attached to the cable you should be able to see whether the cable jacket has moved in its retainer clip or the return spring has failed or is just incredibly sticky.
