Depende del objtivo de la investigación y del método que se aplica: inductivo o deductivo. Sobre este asunto sugiero a Chalmers sobre la ciencia (What Is This Thing Called Science?).
This will be depend on the topic on which you are doing research , if its on consumer data which depends on the timeline then i would strongly recommend to go with additional data collection. This will give your database more diversity and your results will be more reliable.
Yes, the world may well have changed since 2021 (in the midst of COVID).
Yes, your advisor may hold approval power to declare whether you have successfully completed your work.
However, here's a couple of questions to consider:
1. Were the original data collected sufficient to answer the specific research question/s you originally were trying to address? If so, then what is the reason given for the suggestion of collecting additional data? If not, then does the suggested additional data correct any deficiency?
2. Would the additional data suggested address the same or an altogether different research question (e.g., are results stable over time, or were the results anomalous due to the peculiar nature of the time frame in which data were collected)? If it's an altogether different question (such as stability), then is this suggestion being offered to help make your work more attractive for publication, or for some other reason?
I agree with David Morse. Is there a plausible specific reason to suspect your basic results would have changed in 2-3 years due to some historical factor? Is it likely to have a 'large' effect? If so your research question changes from 1) estimating the original effect circa 2021 to 2) comparing the estimate 2021 to 2023. In this case you would need to consider the limitations of estimating an effect in samples of different size that will have different statistical power to estimate the same effect size. In my opinion there should be a sound basis for changing your research objective after you have collected data, and having data that are 3 years old is not by itself one of them.
If there is no plausibly large historical factor to justify changing your research objective I would suggest you analyze your n=390 really thoroughly and list 'possible changes since 2021' as a potential limitation, and list replicating your results as part of your suggestions for future research, in your Discussion section.
But as David indicated you and your supervisor need to agree on all matters. If your supervisor hasn't explained the reason to collect more data, perhaps you can professionally and politely explain to her/him/them some reasons not to. Good luck.
You didn't give the reason why your supervisor wanted to add more cases. Is it because things may have changed? Because you lacked enough cases to support the analysis? Because the extra 50 would be qualitatively different and would provide new perspectives on the data or make your data more broadly generalizable?
A lot of research is based on old data, and 2021 is still pretty recent. For many topics, the age of the data would make little or no difference, but for other topics it is important. Sometimes, even when things do change, you can still present your analysis as describing a particular point in time.
As to how to analyze the data, if the purpose is to see whether there has been a change, then you would want to compare 2021 with 2023. You might treat that analysis as something of a confirmatory analysis to check whether your original analysis was time-limited, without necessarily redoing everything. If the purpose is to increase the N or add new types of participants, then you may be able to combine all of the data together, perhaps adding an adjustment (such as a dummy variable) to allow for changes over time.
As a practical matter, there is an old saying that the customer is always right. If you need to please your supervisor, and a civil discussion does not change his/her opinion, then you may have no choice. Many of us have made changes that we didn't want to make.