From the MDN:

display: none turns off the display of an element so that it has no effect on layout (the document is rendered as though the element did not exist).

It means by setting display: none you are removing an element from the DOM which removes the value you have in it. You can consider using visivility: hidden to hide one of your forms, but in this case, other elements won't take the space of the <form>.

Relevant article: Visibility hidden vs display none – What is the difference in CSS ?