I've read some other solutions but no matter what I tried I still cannot get them to save. Any idea what might be the issue?

Right click the .exes and change the compatibility settings. Disable custom themes on the game. Probably run in compatibility mode for Windows 98.

That fixed it for us, thanks.

On Wwindows 7 32 bit, I dont use launcher.exe, it runs well via RCT.exe. I have it set to compbality mode for Win 98/ Me (Win 95 gives me no driver error) and disabled vissual themes, desktop composition and also display scaling on high DPI settings. Run as administrator too, but I dont use UAC so I guess it does not matter.
All this options did nothing for me, it all runs like if I don't change anything.

In fullscreen at 1024x768 games is bit laggy. After about 10 minutes the save and load dialog stops working and game runs ok.
However it seems in window mode game runs just fine even after 20 minutes. It wont keep me from saving like a maniac every 3 minutes though.

Only bad thing that i noticed is that in maximum size window, the sound gets bit "scratchy" but its window big as 1280x960 or so, so size window around 800x600 is still ok.
Hope this helps somebody.