I was able to find out the reason for my past payment method and account suspensions - and entirely by accident which truly shows the incompetence of Uber and its customer support. In short, Uber payment systems sometimes have trouble processing tips when Uber Cash is used for part payment or the tip is given at a much later time, such as the next day. Uber systems will fail to process the payment but then treat it as if the payment actually failed with the CC company and then suspend the CC and possibly ding the account for fraud.
I only found out about this because my CSR was suspended once again and upon contact with support, the representative described the issue and mentioned offhand that it was the same issue I had previously.
I reviewed my trip history in depth in an attempt to identify the precise trips or orders during which the problem occurred. It appears to be most often when Uber Cash balance is sufficient to cover the payment due for the ride or order, but the remaining Uber Cash balance is insufficient to cover the tip. In that case Uber fails to use the Uber Cash balance or charge the CC and then believes there is an outstanding balance on the account. Another two of the suspensions apparently occurred when I attempted to add a tip more than 24 hours later. However suspensions did not occur in every circumstance so there are likely other factors involved.
What is a bit appalling is that when I reviewed my past transactions it appears that in no cases was the tip I attempted to give ever actually processed. So the driver got screwed by Uber and so did I.
From an ethical standpoint, I'm honestly not sure I can continue to use Uber, $15/month AMEX credit or not.