I understand, but the main issue is that it is not caused by Ajax Search Pro itself. There is no single piece of code that unfocuses the input field, it’s not possible to configure the plugin that way, it wouldn’t make sense at all.
If it’s only IOS the issue, all we have is to keep trying to workaround. I’m willing to help with it, even though it is way out of scope of support.
Can you please check if IOS phones is the only case where the code doesn’t work? I was working on a different feature where I found a yet uknown workaround for asynchronous IOS iPhone input focus which should work very well in this case too.
If every other device works and only IOS is left, then there is hope.