iPod Click Wheel iPod Car Charge/Play Difficulties

I use the a Belkin car charger for my iPod. I bought it around the time I got my then new Click Wheel iPod (Yes, yes, I know it's old). This setup worked well for many years. But recently I decided to change things up and got a Dual USB Car charger, thinking I could keep multiple devices charged at the same time.

Thing is- My iPod will turn on and play for a minute or two, then promptly turn off and on while connected to this thing. It still works well with the Belkin charger, though. Does anyone have an idea of what's going on, or know if there is anyway I can get this setup to work with the iPod- or will I have to stick to my old setup?

I guess it's too old and too specific of a set-up to get a proper reply here. Oh, well.