Hi,
The errors are reffering to two separate files, of which the first is not plugin related, but the WordPress core.
The second error refers to a line, where is no code executed – which may mean that the memory is already depleeted when the execution gets to Ajax Search Pro. Memory related issues are very hard to debug in wordpress.
To make matters worse, this file is only used when a page is viewed to determine if the plugin assets are required. So it uses almost no memroy whatsoever. Generally the plugin requires very little memory to work.
Does this happen on a specific page or in a specific back-end page? Is it possible to replicate the issue?
If not, then there is very likely a memory leak somewhere and the errors were triggered randomly at a point where the actual memory ran out.