Start by considering how precisely you need to know the variability among runs. That should be informed by the differences in sensor resistances you ultimately want to be able to detect among gases. When you eventually get to the point of comparing gases, note the following rule of thumb* for the number needed in each group ($n$) to detect a difference in mean values between 2 groups having normal distributions and the same variances:
$$ n =\frac{16}{\Delta^2}$$
where $\Delta$ is the standardized difference, the ratio between the difference you would like to be able to detect $(\delta)$ and the standard deviation $(s)$ of the measurements, $\Delta=\frac{\delta}{s}$.
So if you only care about differences among gases on the order of 100 resistance units, it won't matter much whether the standard deviation among runs on the same gas is 0.1 unit or 1 unit or 10 units. The rule of thumb says if you only care about differences on the order of 100 units you might get away with single measurements on each group unless the standard deviation is on the order of 25 $(\Delta = 100/25 = 4),$ although you would probably want to do 2 or 3 regardless to rule out some catastrophic error. Note also that this rule of thumb shows you how much different values of the standard deviation would matter in terms of ultimate experimental design.
The reason for first thinking hard about the precision that you need in your variance estimate is that "learning a variance is hard," as @cardinal put it in this answer. The variance of a variance estimate when sampling from a normal distribution goes with the 4th power of the standard deviation and decreases only about linearly in the number of observations, so you need a lot of observations to pin down limits on the true value of the variance. You don't want to spend more effort on determining the variance than is necessary.
I would recommend starting with a pilot study that puts more emphasis on multiple gases and less emphasis on the number of runs per gas. Use a panel of gases likely to cover the range of expected resistance measurements and start with about 4 tests on each gas. Standard linear modeling (analysis of variance) of that type of pilot study will give you information both about likely differences of interest between gases $(\delta)$ and, by pooling information from among the gases, the standard deviation of measurements $(s)$ around the corresponding mean values. You then use diagnostic tools for linear models to examine whether assumptions like constant standard deviation among gases are reasonable, and if needed adapt your approach accordingly.
You might also want to design your pilot study in a way that can help you estimate potential carry-over among consecutive measurements on different gases. This sensor system presumably depends on gas adsorption to the resistive element, which can be quite tenacious and hard to displace. Rather than doing your tests by "waiting several hours longer than necessary" to get some idealized estimate of measurement errors, you might be better off running your tests more like they will be performed in practice and learning early on just how big a problem carry-over might be. My former life as a chemist makes me suspect that in practice that will be a larger problem than the error inherent in the resistance measurements.
*Gerald van Belle, Statistical Rules of Thumb, 2nd edition, Wiley, page 29.
