Hey John Lyman ??
If you have the Pro version you are eligible for support at: https://www.wptouch.com/support/ Get their support there!
Having said that.. I went to: https://www.wptouch.com/support/knowledgebase/optimizing-caching-plugins-for-mobile-use/#W3totalcache
and found these helpful sounding suggestion for using W3 Total Cache:
W3 Total Cache
If you have “Browser Cache” enabled, please disable ‘Set expires header’ in the Browser cache settings to prevent Desktop/Mobile switch link issues.
Go to the “Page Cache” settings under the Performance tab.
Copy the list of mobile user agents found in our list of “User agent list for configuring cache plugins“.
If you have added support for additional mobile devices in WPtouch Pro’s Compatibility > Custom User Agents field, you must also include those user agents in the “Rejected User Agents” area in W3 Total Cache.
Scroll down to the “Rejected User Agents” field and paste the list of WPtouch default user agents, adding one per line.
Save your changes.
Go to the “Minify” settings under the Performance tab.
Scroll down to the “Rejected User Agents” field and paste the list of WPtouch default user agents, adding one per line.
Save your changes.
Go to the “CDN” settings under the Performance tab.
Scroll down to the “Rejected User Agents” field and paste the list of WPtouch default user agents, adding one per line.
Save your changes.
Finally, go to the W3 Total Cache “Dashboard” and select “Empty All Caches”.
Your site should now be configured correctly to work with WPtouch Pro and W3 Total Cache.
If you are running a version of W3 Total Cache released before version 0.9.2.9, you will need to add the wptouch-pro-view cookie in the “rejected cookies” area in the Page Cache settings.
exclude-wptouch-pro-cookie
Exclude WPtouch Pro Cookie
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Hope this helps ??