There is a def-var for dialog history size, def_maxdialoghist, and the default is 10. It's not currently listed in Options, but you can use set-var on the SlickEdit command-line (or Macro > Set Macro Variable) to change. It is a global setting, there isn't a way to override history size per form, but something we could definitely think about for the future. (On a related note, see def_maxcombohist specifically for Combo box controls history for the drop-down). YMMV.
Separate history per tab? Interesting idea, especially for this form. That could be a possibility in a future build.
There is a feature to save and restore searches, useful for "bookmarking" searches that you might use infrequently with complex setups or gnarly regexes you don't want type again. Saved Search Expressions menu is available on tool window on the right-click context menu, and on the menu drop-down in Mini-Find. From that sub-menu, you can save all current options using the Save Search Expression, and recall them later as needed.