I agree with Jay on all points he makes, and in that I've discovered it best to simply dump air all around for storing the rig next to our house. That rids me of the annoyance that comes from watching it gradually sag on one side or one corner. Plus, there can be more than an annoyance involved if the sag puts a twist in the coach frame; such a twist contributed to, but wasn't the root cause of, the cracking of our windshield the first winter stored next to our house. So a word of caution here, even though all bags end up even after full air dump, be sure your parking spot is not too unlevel to begin with.
We don't have hydraulic or electric jacks, though our old coach did, and I found them problematic over 21 years, so didn't want them on our Beaver. However if you have them, they certainly are an option, and can help "unload" tires a bit during storage. Our Monty Rae is just a smidge off level on her pad, because I've found that at a certain "level point" rain water enters through a gap in the windshield surround seal over the driver's corner. Loren at Bend looked at it a couple years ago (months before I noticed water on the dash one day), and pronounced it okay; so I've got to get it back to Bend for a fix. In the meantime it' fine as long as the rig is imperfectly level.
That's a bit off-topic, so as previously advised, Mel, I'd simply dump all the air for storage. Techs don't like looking for microleaks in the air system as they can be time consuming and difficult to pinpoint, and labor can be costly. If the leak point isn't obvious and its effect isn't callamitous, most people don't fret it much. If you leave your battery switches on in storage, the auxilliary pump can help keep things level, activating when the rig sags off-level as prescribed by your air level controller, but most of us turn off main switches for storage. Full dump is just easier.
If the rig comes to level upon engine start and tank air pressure builds to full, then you likely have no worry regarding Travel Mode; the leak is not significant enough to overcome the coach air supply, esp. since you said it takes weeks to deflate. Driving the coach should keep plenty of air available to maintain comfort and handling characteristics. There is likely a microleak somewhere in the components or lines involving the right side module, since you say the whole right side drops, not a corner, which would zero in on a bag or its lines.
If it still concerns you, depending on your locale, I'd have the guys in Bend check it, or at Alliance Coach in Wildwood, FL, or have it checked by a tech while at the FMCA convention or BAC rally this summer, or even at HWH in Moscow, IA.
Joel