A common advice for storing passwords is to store them into an encrypted file, for example by using a dedicated software such as KeePass2. To keep this file in sync between several computers, the advice goes, the file is put on an online storage such as Dropbox. I have seen this solution proposed many times as an alternative to using browser plugins such as LastPass -- and perhaps is it indeed a superior solution.
In this scenario, I think, the online storage itself is not considered secured -- it is supposed to be either hackable, or itself actively eavesdropping.
Yet from what I understand from some answers read here, it is not safe to encrypt several files with the same key. And of course, a file containing passwords is deemed to be updated regularly.
So my question is, should we consider that having access to a (large) history of an encrypted file when this file is encrypted with the same key is a security flaw? Is this a general rule or are there encryption algorithms for which this is not that a problem? What about KeePass(2) more specifically and what to think about the advice above about online storage of kdbx files?