I hate to say it, but the 'autopot' style of hydro system may be making your troubles worse. Remind me again if you have aeration in there?
Let me give you some background on the place of perlite in a hydroponic system. I'm NOT an expert by any stretch, but these are the situations in which you are most likely to encounter commercial growers using it:
-As a lightener for a coco coir grow
-As a medium for starting cuttings
-As a medium for growing root vegetables or fast-cropping leafy crops in a flood-n-drain system that allows for COMPLETE drainage between flood cycles. (Yes, I spend too much time reading Growing Edge haha so sue me)
You never want your roots sitting in the solution unless it is being AGGRESSIVELY aerated as a DWC grow. You can fertilize all ya want, but with insufficient oxygenation to the root zone, the plants can't do much with their food, like giving a calzone to a dude with no teeth.

So. Given what you have there, and trying for minimal root disturbance while you are troubleshooting... I'm going to suggest adding some serious airstones to the reservoir. If you can't guarantee complete drainage, you are going to have to suck it up and build a hybrid between that style and a DWC style to deliver O2 to the root zone, or completely re-think the system.
Just out of curiosity, how many gallons does the res on that thing hold, and how is the water transferred to the inside of the pot? I hope it's not a wick system; if it is, I don't know what to tell ya other than lose the whole autopot and convert to an automatic drip-to-waste with good drainage. You should have at least a couple gallons to do this right. Stick an aquarium pump in the res and use weedhound's basic sick hydro plant schedule:
Distilled or RO water, add CalMag Plus to 300ppm, add a stand-alone base fert with micros to 600ppm, adjust pH to 6.0, cross your fingers.
I think those plants are too weak to take clones at the moment. The clones are unlikely to survive.