If your issue is the holding period "sensibility", I don't have persuasive economic/fundamental motivation about it. It's an interesting question. Anyway in econometric point of view the issue is part of instability parameters problem. If the time horizon for your investment project is, for example, one year, then you need return and beta one year based. Therefore, in simplest way, you have to take yearly data return to estimate the beta, with certain historical depth. However the beta are not (explicitly) time horizon dependent and you can take the monthly/weekly/daily data. In my experience the time frequency are not so important in beta estimate (also if the number of observation change and this tend to suggest, at least in my opinion, weekly or daily data ... but monthly are largely used).
In opposite is so important the historical depth. This problem is strictly related with time varying variance and correlation. However the "beta structure" and experience suggest that it move around one and this fact alleviate the problem. You can see for example Blume's technique. Maybe if your time horizon is too long the better choice for beta becomes 1.
In any case, for example and at least in the past, Merrill Lynch suggest to use monthly data with 60 obs. In the past I looked for but I'm not found empirical research for support them choice.
Hope that helps