My daughter has a 90 Miata. It keeps loosing/using oil... I cannot seem to find a "leak" and it doesn't seem to burn oil (no blue smoke coming from exhaust). Regular checks of the dipstick and we always seem to be adding oil.. any suggestions

John, how much oil in how many miles, and how many miles on the motor? A motor can use oil and not blow blue smoke!

Just over 100000 kms on the car. Unfortunately I have never really track the number of kms before we have to add oil... but I would be suprised if it was more than 5000km

Assuming that you did mean 5000ks and not 500,You probably should be changing your oil { and filter} about then and not just topping it up! You said you're "always" adding oil, but every 5000ks is only about 1 to 2 times a year on your ks! I'm reading between the lines a bit and thinking you don't have a very good maintainance program for that car! Have you noticed an increase in the consumption over a period? Young drivers can put high demands on an engine and together with old oil, which is full of contaminants,it can appear to be using oil more than normal!Change your oil and filter now using good quality{not Mobil 1} and change them again at the next interval {from your manual} and see what happens!I don't think your motor has too many problems at the moment unless I'm reading it wrong!