Keep session data after 3rd party script is loaded?

My code executes as follow -
1) a Search page is loaded where session was already started, var-dump() shows the correct session info like username etc.
2) User enters a search value in a 3rd party script search box that forms part of my search page, I have no control over this script. 3) User presses the enter button, my javascript listens for the press event - key13.
4) The search criteria is then passed to a PHP page that adds values to the current session, which is then returned to the search page.
5)This is where the problem arises, when then user pressed entered, the 3rd party script executes additional shown data maps, it refreshes the entire page and my additional session data is lost. -By lost I mean the following - If I do not run the 3rd party script, I get the additional session data back into hidden inputs - var_dump() shows the data correctly on the search page, no problem, if I run the 3rd party script, the only session data that is returned is the login data from the beginning of the session.

I need this data to perform additional data enquiries, so my question is, how can I still keep the session data even if the 3rd party script is refreshing my page.

I tried to add it to its own form and used ajax to load only that form, did not work as it seems the script overrides my code. No errors is returned as all code works as it should, just the refresh that looses my returned data. I used alert to see if my javascript is running, no alerts where returned which means that mine was not running. Without the 3rd party script, I get a return on all the alerts.

I also tried to run the script in different parts of my page, still the same return.