I personally have never been to Teesside Airport but I have read a number of threads on this forum about the station and researched online. It has shown that the Airport it's self has seen a large decline in passenger numbers and the number of destinations, both Charter and Scheduled Services. The pulling out of Ryanair, Thomson and other large Airlines is likely to be the reason for this and today there is simply no demand. These low passenger numbers at the Airport (161,092) and stated by Starrymarkb a maximum of 325 passengers per day simply mean that the Airport's station will suffer too. The website does not even state Teesside airport station as the closest station, but Darlington 7 miles away. This shows to me that even the Airport, from which the station serves, have no faith in the Station!
You state in your petition "This route has many passengers but do not realise the station is 'their' (Grammar!)'" and you state this before in your appeal also. However I should Imagine the passengers know the existence of the station but have no requirement to use this. Should the number of services increase (Which would probably not be a viable plan) then there would likely to be a small increase in passengers but not a sufficient increase as many of the passengers would not use the station due to the location of the station.
Now it appears that there are plans in the future for housing developments, however as it stands the demand is not enough to increase the service. I believe the airport has a friends group to give the station "some tender loving care", which you could contact to give some ideas to them and see what becomes of that. However I do not believe a petition alone will help save Teesside airport station. :roll: