Automatic transmission odd behaviour on shallow inclines

I have a 2007 Renault Clio with the 1.6l engine and automatic transmission. Lately I have been experiencing a strange issue where the transmission sometimes does not automatically shift into third gear when going slightly uphill – I can get way past the point where it should have shifted and still it stays in second gear. The problem seems to happen consistently on the same few roads and in each case I can normally shift up manually using the paddles on the steering wheel and carry on as normal. It always was a bit hesitant to change up on certain hills but it definitely feels like it has gotten worse in the last few months or so.

The gearbox (the DP0 model I believe) otherwise seems fine and goes through all the gears as you would expect. I’m guessing maybe there is a bad sensor inside the unit itself or in the engine. There are no fault codes from what I can see but I can’t check the fluid levels unfortunately. I did replace the battery yesterday since it was on the way out, but it doesn’t seem to have resolved this issue.

The nearest automatic transmission specialist is over 30 miles away so I can’t easily book it in and due to the age of the car I would rather have some idea of the problem first if possible rather than pay for expensive diagnostics that may prove pointless if repair is not economical. Any suggestions would be appreciated