Good news first: the free version supports more than one booking field per form. If a second DrezSync Booking field is not working, it is a setup issue, not a version limit. Here are the usual causes, in order.
The field has no calendar, or the wrong one
Each booking field needs its own Google Calendar ID. If the second field is blank, or points at a calendar with nothing open, it shows no times. Open the field settings and confirm its Calendar ID is set and correct.
A cache is serving the old form
If you just added the field and it is not appearing or behaving, a page or plugin cache may be serving the previous version of the form. Clear your site and any CDN cache, then reload. See Changes Are Not Showing Up.
Conditional logic is hiding it
If the field is set to show only when another answer is chosen, it stays hidden until that condition is met. Check the field’s Gravity Forms conditional logic.
Its days or hours rule out every slot
A field with no open days selected, or hours too narrow for its slot length, shows no times. Confirm the second field’s own days, hours, and slot length. See No Available Times Show on the Form.
Related
Setting up more than one field: Adding Multiple Booking Fields to One Form. Stopping a person picking two clashing times, a Pro feature: Overlap Protection.