Dear colleague,

What do you mean by stability for collecting data? Can you be more specific?

If you mean stability in the sense of reliability of the data, then it depends on what are you going to do with the data. What kind of analysis you intend to make. Many measurements use the standard deviation, sigma = sqrt(1/N sum_N (X_m - X_i)^2), to estimate what size, N, the data should have to present statistically reliable answers. But that is not a iron rule.

On the other hand, if you mean stability over time, The researcher can not infer that from empirical data, as in nature, even in controlled environments is hard to say that the phenomena of interest will ever manifest without contamination of external factors . What you can do is estimate the validity time-scale of the experiment. For example, we do not know for sure whether a proton decays or not, but experimental evidence says that it do not over periods up to 1.67×10^34 years. From less exotic phenomenon such as merchandise preferences of a given population, energy consumption, opinion pools, etc. what you can do is measure the same system sequentially to understand the statistical tendency of the system and infer the time-scale of validity of the answers you obtained with the data in question, or to predict when your results will fail.

I think you refer to secondary data posted onto the website. You have to use your judgement on whether that website is maintained by a respectable organisation and then you can use that data and quote the source. For example, I used this site for Covid-19 secondary data

https://data.humdata.org/dataset/novel-coronavirus-2019-ncov-cases

World Bank is another reliable source for secondary economic data

Conduct the EDA on the data and cross-verify with the description and with its Source or publisher. you can also collect or download the data from reputed research labs of various universities' websites where they provide all the information on how they have collected the data and its authenticity.

In addition to the answers above, my initial interpretation of your phrase "...the stability of a site for collecting data..." is the consistency of being able to access respondents.

For instance, when I was exploring data collection sites for my Master's research in the drug use and addiction field, I rejected self-help groups because participant attendance at them seemed (to me) more sporadic than attendance at government-funded drug rehabilitation service outlets; indeed, I ended-up collecting data at one of these latter providers.

Thus, it's a judgment call.

in industry, we use % of availability of the data source. Time available / total time. The source by it self is generally stable, as an ERP.

Seems to me that a fundamental question for the researcher, in regard to a potential data collection site is: can I get the data here?