Please add anything I missed. I don't know much about these vehicles, this is based purely on 3 days of research, so please correct me where needed.

Note that this information is from forums, not just this one, and obscure pages deep into Google indexes by real owners and techs and mechanical engineers.

Statistically speaking most people sale their caravan or pay to have transmission work done, and often times it's just one or two of these issues that costs a few hundred USD tops to fix. Tranny work by a pro averages >$2,000 and with this problem and these models they almost never fix the actual problem, so you end up paying over 4k in repairs on something with a $1,100 blue book and still have a unreliable vehicle...

What causes slipping transmissions(at least for dropping to 2nd and not hitting 1st without braking and light rev on 3rd gen):

• Corroded battery terminals, low battery, wrong battery
• Loose or corroded TCM socket connection(clean and grease)
• Loose or corroded TCM ES01 splice connection(uncap+grease+recap+wrap)
• Loose or corroded TCM ground(clean and grease)
• Worn, jammed, corroded, or broken trans valve solenoid($150-$200 new and relatively easy to replace)
• Filter or shift map worn or clogged(<$200 rebuild kit at advance auto, or better Mopar master kit for around $140, 41TE=R0000413AB, 41TEs=R0CPT403AB)
• Heavy particles or too little fluid or wrong fluid in trans or torque converter(flush and fill with ATF+4 and change filter(holds up to 9 quarts))
• Cylinder shaped plastic piece inside trans. I forget what it's called now and can't find the source again, but a mechanical engineer once tore down a lot of failed a604 trannies and these were typically the cause; they were all cracked. There is an aluminum replacement. I will update this when I find the source again..
• Short, bad controller, or bad ground not related to TCM bus(I think this can actually happen, if it's controller board there is no economical way to trace it, if you're lucky PCM/ECM scanning finds it, else use a probe on the wiring system(the wireless ones are best and <$200), there are scenarios where neither of these work(like controller with burnt resistor, broke solder, or bad connection), a lot of scenarios actually. Clean and grease EVERY ground to at least have a fighting chance at tracing it)

In my research I found most owners took their vans to pro shops who repeatedly failed to fix the issue even with manufacturer assistance.. Say what you want about this post, but it's free and probably more likely to work and not pay what you'd pay for another vehicle trying..