There are two things you have overlooked.Doing some calculations and it seems a unit drawing 65w off through a Victron 500w pure sine inverter a 95ah battery could last up to 17 hours of the battery is in good nick. Battery capacity = 95Ah x 12V = 1140 Wh. Using the formula to calculate the battery life: Battery life = 1200Wh / 65W ≈ 17.53 hours
Firstly as has been discussed previously in this thread, a battery is rated to have maximum State Of Charge quoted in Amp Hours (Ah) You tell us your battery is a 95Ah battery.
It is recommended that a Lead Acid Battery should only be used to a Depth of Discharge(DOD) of 50%. in your case that means only using 48Ah. If you go below 50% there is a rapidly increasing probability the battery will be damaged or have its working life significantly reduced.
Given this information it points to halving your available run time to about 8.75 hours.
But there is more to bear in mind:
As batteries age, their ability to hold 100% of their stated capacity diminishes. I suggest a Lead Acid battery might lose 10% of its capacity year on year
You would expect a new battery holding 100Ah of capacity should last 100 hours if it was delivering 1 A continuously. If you double the current draw, you might expect the battery to only last 50 hrs. Unfortunately if you increase the current draw the battery has a harder time producing the current, and it actually does reduce its overall capacity and it might only manage 48 hours at 2A. I can't give exact figures as there are so many variables, but if your system is drawing enough current from the battery fo give you 65W which divided by a nominal 12V means it will be drawing 5.4A , then there could be a noticeable reduction in the length of time the battery can drive your TV
I would expect that with all these losses your 17.53 theoretical run time could in practice be down to 7 hours (or less if the battery is not in good condition) , before the battery voltage is too low to drive the inverter.