There is a spring in most of the units that pulls the flapper and foot lever assembly back into place in the closed position. Also, the pivot surface areas of the lever/flapper assembly can, on occasion, get corrosion built up on it, which could also cause the flapper to stick open.
My recommendation is to access the flush mechanism under the toilet and check the spring first. From there, try some lubricant such as WD-40 or some white lithium spray on the pivoting/moving parts. If that does not work you, you may have to replace the flush assembly.
And yes, you'll find those ubiquitous Aqua Magic's in most <100K RV's and travel trailers, because they're cheap. You also get what you pay for too.
Personally, I never liked that Thetford Aqua Magic plastic POS, and replaced mine with a Sea-Land Model 511+ Traveler porcelain bowl toilet with a real wooden seat. Feels like your actually sitting on a toilet instead of a 5 gallon plastic bucket. Also much more trouble free and easier to clean than the plastic toilets. If you do upgrade, don't forget to order the 2-bolt to 4-bolt conversion base ring. The cheap Thetford Aqua Magic's have a two-bolt mounting base. The real Sea-Land toilet has a much sturdier 4-bolt base mount. A pretty simple straight-forward swap-out.
(You'll find the conversion ring in the same link, right below the toilet.)