The thermostat on my 13 year old Rover 2.5 V6 got stuck shut about 3 months ago and to be honest I did drive the car whilst overheating albeit very carefully for about 6 miles. I had the thermostat changed by a mechanic friend of mine. At the same time he changed the radiator which was showing signs of its age. The water pump was alright it was changed last year. Since then I need to add half to one pint of water every few of days. He took the car back and pressurised the system and left it for about an hour it showed no loss in pressure. There is no external leak or paddles under the car that we can see.There is no water in the oil that we can see and there is no loss in engine power. It is very strange. Any suggestions will be appreciated.
The only way coolant can disappear without a trace, unfortunately, is through the engine, either a head gasket or cracked head allowing the coolant to go into the cylinders where it is emitted along with the exhaust gases. The only fix once you are fairly certain this is what is happening is to pull the head off and determine whether it is a blown gasket or the cracked head. Possibly a compression test could help diagnose this. The mechanic's pressure test was a good idea to check this also, but if a very small leak, might not have detected the problem. Same with the compression test, might only show up very minimally at full operating temperature. Keep a record of how much coolant is lost for your mechanic to help him diagnose this.
Look for coolant stains in the V of the engine, and around any coolant pipes. slow leaks here evaporate away leaving the coolant residue behind. If using the OAT red coolant then look for pink staining. Was the coolant pressure test done with a hot or cold engine? Some leaks can open up (or close up) as the engine warms up.
Added from Comments: Pressure cap 'o' rings are also a possible culprit and aren't expensive to replace - look for viton ones.
I had a car leak without a trace. Full radiator, drive at 50 mph for an hour- full radiator, no leak. But; drive at 65 mph 15 minutes and it overheated and radiator was very low . It was the water pump , at certain speed the fan/water pump (one shaft) vibrated, water leaked and was atomized by the fan so no trace of leakage. I found it by accident , I was looking around the water pump and leaned on the fan blade ,it moved too much because of a bad bearing and seal.