Can a simmerstat switch be fixed? And how?
According to oxfordparts.com.au the part has been replaced/superceeded by TD3V-800K which I think is still available. I found a bunch of eBay listings anyways. 

Also worth checking out this. If it looks the same as the switch you have it's probably the same 

https://stoveconnection.com.au/shop/index.php/store/stove/controls/cooktop-controls/tl-205.html

Be aware the TD3V part might not look identical but the connections should be the same. Likely they improved the "guts" so they don't fail so soon...
Or so that they're cheaper to build. 

Don't try to fix the switch, it'll never be right and you could melt stuff. Not to mention it's likely glued together.
Good luck!