Some companies will not update their tex distribution regularly.
What is a practical length of time to allow to pass before failing to resynchronize
Tex Live or
Miktex could reasonably become a hindrance?
I don't think there really is a single answer to this question, but rather than have multiple answers that just say "I do this", I'll try to lay out some of the criteria that you might use to decide. Furthermore, there is an important distinction between updating the binaries of the distribution vs. updating the packages within it. For TeX Live especially, the binaries are updated on a yearly schedule, but packages for a given year can be updated continuously throughout that year. For MiKTeX, binaries are updated throughout the year as are packages.
First off, the core TeX engines and packages are remarkably stable and relatively bug free, so it's quite possible to use the same distribution for years and not encounter any problems at all.
Because of this fact, a very reasonable strategy is to only update your distribution if you encounter a problem that is solved by a later distribution. This strategy might be especially useful if you are working on a large project for which stability is important. (Writing a dissertation comes to mind here.) This is also the strategy that commercial software users typically use. If the current version works for the required use, then updating has no value, and may induce problems because of changes in the new distribution.
A strategy related to the one above is to update only when new packages or updates to packages show up that give you added features that you find useful. In this case, it's always best to update your entire distribution rather than just the package you are interested in, since new or updated packages will typically assume the most recent distribution, and updating just a single package will likely lead to problems with package dependencies. Furthermore, at least with TeX Live, you cannot update single packages in an older distribution using the current year's packages.
At least for TeX Live, the binaries of the distribution are updated only once per year, and for this reason, many people update on the same schedule. (See Why does TeX Live "require" yearly updates? for details.) The advantage of this method is that you will always have the latest distribution, and for that year you can easily update all packages within the distribution any time you need. As mentioned above, since the core TeX engines and packages are quite stable, updating each year rarely causes problems with backwards compatibility.
Since disk space is cheap, it's also possible to keep multiple years of TeX Live installed on your machine. This combines the best of options 1 and 3. Install the current year and if your critical projects that depend on the older distribution don't work, keep that one around for those documents. With the Mac version of TeX Live for example, this is trivial to do, since MacTeX comes with a way to change distributions via the system preferences.
I think for most individual users, Option 3 is the most practical unless you have particular reasons for keeping an older distribution around. If you encounter problems and ask for help (here or on other forums) most people will assume that you are using an up-to-date distribution. Furthermore, for some large package that are being updated regularly (e.g.,
biblatex, TikZ) and those that depend on the LaTeX3 code base (e.g.,
siunitx), it is typically important to have the most up-to-date versions of everything.
Whether you have particular needs that would require the very conservative Option 1 will really depend on your use case. If you are auto-generating LaTeX code from a web page or external application, stability is probably more important than the latest stuff.