For the first time in my life I'm playing Spyro, the original from 1998.
I played around 20 minutes in the starting fields, found the required ten dragons to go on the hot air balloon but then I had some real life problem and I had to turn off. In all the playtime it didn't ask me to save and once a dragon freed said "the game saves a check point every time you free a dragon".
On what are you playing? OG consoles need a memory card to save to. Sorry if this is known to you but more information is needed to diagnose. (I looove the spyro trilogy, both the original from back in the day, and the remake)
Hm, perhaps double check if there's any settings you may have to adjust. Then as the other user mentioned try testing the save-at-dragon-statue. Also maybe try playing /saving a different game just to test if the memory card is working properly too
I'm pretty sure it did autosave in world transition like the other poster mentioned but definitely not the regular autosave intervals that are more common today. I could be wrong about that but I'm not sure why the transition save isn't working for you. Regardless, glad you could get some save functionality working.