There is no simple answer to this, but the reasons are quite varied.
Advertising. The Action Force range suffered from extremely bad timing as far as a cartoon was concerned. About two years earlier, Palitoy had attempted to get an Action Man cartoon off the ground, but were told that under the (rather antiquated) UK advertising rules of the time, that because the Action Man range was well established, a cartoon would amount to advertising. Action Force was seen as an extention of the Action Man range because of the 1982 figure range which were basically 4 inch versions of Action Man advertised under both banners.
"Ah!", I hear you say, "but what about He-Man, MASK, Thundercats, Transformers, etc?" They managed to get around this by releasing the toys either at the same time as the cartoon, or once the cartoon was on air. The big problem with these cartoons was that they were advertising the the cartoons during the commercial breaks. This led to a backlash from the public (for this, read mother's pressure groups, as per usual in this country

) and the advertising rules were tightened up even further.
The state /quality of cartoons in the 1980's. This always makes me cringe. British cartoons
were being made, but they tended to be exclusively children's fare. Like Dangermouse (best Brit cartoon ever made! Any non Brits on here, look it up on YouTube. You won't be sorry!) and Bananaman. Yes, my American friends, Bananaman. That was good, too. But they were aimed at children. Like in the Warner Bros and Disney cartoons, realistic violence was frowned on. American Saturday morning toons were heavily censored and dumbed down, and we cut them down even more. When Turtles made it across here, the word Ninja was changed to Hero and any scenes with nunchaku were edited out.
Let's say that we had managed to get an Action Force cartoon. Would you have put up with Z-Force and SAS Force using lasers and being worse shots than Cylons or Imperial Stormtroopers? Or being like the A-Team? 10, 000 rounds of ammunition being fired; casualties: 0. The comics gave us realism that was absent from any but Japanese cartoons of the time, with even the good guys being killed in teh line of duty. Let's be honest, and I know that Jamar will shudder at the thought, if a cartoon had been made, it woukd have concentrated on Space Force and outlandish science fiction storylines, and characters like Skeletron and.......The Kraken (will someone please stop Jamar foaming at the mouth at the thought of this?

) Just remember that Return of the Jedi had just come out, and the Star Trek films were doing well at the cinema (well, the even numbered ones

). It would have needed this to sell it to the American television market, and Skip would have probably ended up as another Duke. The first miniseries would have probably been a remake of the Bond film Moonraker, with every Red Shadow shot making a miraculous escape from death and a big battle in space at teh end.
GI Joe/Hasbro. Palitoy borrowed heavily from the GI Joe range, even in the early waves. By 1983, there was a Joe cartoon, even if the Joe toys were not available outside of the USA. Palitoy would be using the range under licence and would probably had to live with restrictions on what they did with merchandising. APC, MOBAT, VAMP, Wolverine plus repainted versions of Cobra Commander and Snake Eyes.
So it is a shame that we did not get a cartoon, but reflecting on the mores of that era, I think I am rather glad that we did not. At least I have the memories of the comic unspoilt.