Hello - I'm looking for a web based shopping cart
that would enable me to:

1. Bill my members once per month, automatically
2. Enable a fr-ee trial, or at least, $1 trial period of 14 days
3. On FAILED rebills, I want the rebill attempts spaced apart
several days.

...I use 1shoppingcart.com currently and they rebill only twice,
on consecutive days following the original failed rebill (this
should not be the case - rebill attempts on failed billings should
ideally be spaced out at least 3-4 days for better results).

Any potential solutions you have are greatly appreciated!

Thanks

Are you going to use this for web hosting ?

If is going to be use for web hosting i recommend ModernBill or LPanel, they have exactly what you are looking for.