I found that jumping it with the negative clamp directly connect to the negative terminal gets the car stated again.
Your statement implies that if you're not directly on the neg terminal it won't start again. Is that true? If so then the issue is with the cable circuit of the starting system rather than the battery.
I said 'cable circuit' since from what you wrote my assumption is that you placed the pos jumper cable directly to the battery pos post and the neg to the neg post. This means it could be the pos cable(s) to the starter, the neg cable from the battery to chassis ground, or a ground strap from the chassis to the engine. If any of these cable connection points are corroded, or if the terminals of the cables aren't all tightly secured to the connection location or even the cable itself (lug loose), in any one of the cables, you could see the symptoms you're seeing.
My trusted mechanic basically told me if it’s not happening with him he will not be able to know what’s causing it.
This is only because not all mechanics bother to theorize a bit and want to limit themselves to a brute force approach.
I once flew across the country to work on an IBM mainframe experiencing weird intermittent issues. Others already tried to troubleshoot it and were perplexed. I shot it down to a power buss bar that, although everything was tight, had just enough corrosion in the connector block to create some resistance and every now and then, depending on the power load, which depended on what the mainframe was processing at the time, dropped the voltage enough to cause a failure in one of the circuits, which in turn caused the system to go down.
The moral of that story is that power problems can sometimes be elusive to determine but applying some theory can help resolve the issue - such as proactively disconnecting each power circuit cable, cleaning the mating surfaces, and checking that the lugs are tight and not themselves corroded. This can be a pain since it needs to be done at any connection point including on the starter, the engine grounding strap, and anyplace else that applies.
Localbar - I've seen pics you've posted of your MDX and there appears to be plenty of corrosion on it, given where you live, so I'd be extra suspect of what I stated in that environment. Worst case, you might want to buy new power cables all around and just replace them, but you need to get them all since it only takes one bad connection anywhere in the circuit, both pos and neg, to create the problem.