For how much time do you usually let your money invested in a casino before finish or renew it?
There is not specific time in doing it, you can only estimate it based on the performance of the site. By setting up a goal in terms of profit and loses, you can make a good decision on what to do with your investment. It is not automatic that you will profit from gambling sites investment, there are sites that does not perform well, thus you have to divest your investment and transfer to a more active sites.
If you invest money in any site, you should keep on track your investment not in a daily basis at least 3 to 4 days you have to check. Becasue the site's performance are not always same, the profit giving sites will run in loss sometimes. In that time if it continues long term we have to move our funds to another reputed sites these are the problems we face in investment.
If the site is provably fair, in what way could the losses continue for a long time?
Say the house edge is 0.8%, you should see those percentages in your investment, depending how much they pay out to investors.
That's why I would recommend investing in Crypto-Games, they're the most transparant with their stats and what they pay out to investors.
The numbers just make sense if you see your investment after a month or so.
So you are recommending checking your investments every month? Not just in a day or two? I haven't tried investing because I haven't had any money yet to invest. It's better to spread your money, and not just put your eggs in one basket. We all know that phrase, I think.