A common issue with gel packs is the latch. Sometimes latches can stick, jamming the gel pack in the compartment and not releasing it at all. This is one of the easiest problems to test because most latches have a manual release. Use this manual release to close and then open the detergent compartment yourself. If the latch appears to stick and the compartment stays fastened or only partially open, you may have a rusty latch that needs cleaning.
In other cases, there could be something wrong with the timing mechanism that controls when the dishwasher opens the detergent compartment. If your dishwasher has such a cycle, it may become stuck at a certain stage or the signals to open the compartment may not be going through. This may be occurring if the latch works but the compartment remains fully closed. In this case, you may need to begin using gel packs that you can add to the dishwasher immediately without a time release.
Sometimes detergent compartments are located in spots on the dishwasher door that cannot open fully when large plates are blocking. For grain detergents, this may not be an issue; for gel packets, the door may only be able to open a fraction, not enough to allow the packet to dissolve. Only line up smaller dishes around the compartment to see if this solves the problem.
In other cases, the gel itself may be the issue. The gel may be melting out early and jamming the compartment or may become glued to the inside of the compartment. You may want to try different gel packets or other detergent pellets to see if any other option works better.