How to have independent Save buttons on multiple panels?

If you're doing this in a workflow, make the task form LOOK like the Item form and have them make their changes there instead of having them open one form just to go to the item form to make changes.  Doing this will allow you to set different required fields as well.

Currently its not possible to put a "save" button on each panel because the entire form must be submitted to "save" the data to the list. 

Also, you cannot force a control to be required in the normal sense. My recommendation would be to use rules to run a validation on if the control is empty.

We are working on a new rules engine that will enable this and more, but that is not something that is currently possible. May I suggest looking at a different way to potentially allow the user to input information. 

how do you keep track what step/stage your are currently in?

how do you recognize, when somebody opens the form from a link, what controls/panel/section s/he should fill in?

do you hide or disable (currently) not relevant panels?

these kind of scenarios use to be handled with a "tabbed form" where there is an extra control (eg. choice) which keeps track of current stage and controls other actions within the form.

if you eg. had an choice with options like 'Step A', 'Step B', etc. then you could configure a validation for 'Column3' control like

CurrentStageChoice == 'Step B' && IsNullOrEmpty(Column3)

so that it doesn't prevent to save form in 'Step A'

see an example in KB

https://community.nintex.com/t5/How-To-s/How-To-Create-Tab-Like-Functionality-In-Forms/ta-p/86705?collapse_discussion=true&q=tabbed%20form&search_type=thread

or further similar topics

https://community.nintex.com/t5/forums/searchpage/tab/message?q=tabbed%20form

Having a form with tabs is quite possible and using them on the edit form is also quite possible. However the form only has one save button. If you want to save different sections, you can do that but the save button does one thing, write data back to SharePoint.

I'm not suggesting you cannot have tabs or different sections of the edit form, I've done plenty of those. However, It was only one save button. So I used panels to show/hide data, had tabs to navigate a user and then the one save button to save whatever was inputted into the form at the correct time. 

It is possible, so yes it can be done, but not with multiple save buttons. I mean in theory you could have multiple save buttons, but technically they all are calling the same function control "save and submit". You won't be able to save and stay unless you use the Save As function which I do not think was rolled out to on-prem yet.