Is there a generally accepted maximum number of times you should split and reseed mammalian culture cells before restarting cultures from new stock?
This is a very good question and it highlights a very frequent misconception about cell culture and it is using the passage numbers as an indication of how well a cell is behaving. Although this can be a good barometer but it is misleading. Passaging can stress the cells if performed very frequently, although again that depends on how fast the cells are dividing.
You should not think of passage (and cell culture in general) in terms of the procedure itself but in terms of population doubling (PD) which can be calculated using the formula provided here (http://www.sciencellonline.com/site/techsupport.php). I personally use [Log10(harvesting cell No/seeding cell No)/Log10(2)]. This should allow you to characterise your cellular behaviour between every passage and allows you to draw a cumulative PD graph. Once the cumulative PD versus time becomes non-linear, then you would know that the cells have changed behaviour and it might be best to use a fresh stock.
The main advantage of this method is that you are not relying on guess work and deal with solid numbers and allows you to predict when you should expect to start a fresh batch for passage. Although passage numbers can do the same job if you assume per passage, the cells have done a certain PD but this is more of a guess work and you can not track how well your cells are doing at a given time point. For example one of the main problems with using a passage as a measure is that you can passage the cells at 98% confluence to a fresh flask and although that counts as a passage but it is pretty uninformative in terms of cell behaviour and gives you no solid numbers and you can do this many many times and although you would have done high number of passages but your cells would appear ok. Although such an exercise is pointless and will probably stress the cells but it is just to make the point that passage numbers are not necessarily a very informative and quantifiable measure of how well the cells are doing or behaving hence PD and cumulative PD should be used. Another advantage is that since you are dealing with actual cell numbers, if you changed your cell culture flask size from lets say T-75 to T-25, you don't have to be worried about changes to your frequency of passage or having to make further guess work on how that has effected your cell behaviour.
My main advice is that you should keep you frequency of passage the same at least in the beginning (although keep an eye on the cell density as you don't perhaps want to let cells to be too over-confluent or unconfluent when passaging, depending on your specific methodology and what has been established in your lab), but count your seeding and harvesting density (cell No) and calculate the PD and cumulative PD and draw a cumulative PD vs time graph and monitor the behaviour of cells. This should give you a good indication of you cellular behaviour under the conditions you are working with them since guidelines are just that, guides and they can never substitute experimental characterisation of your cells under your conditions and handling method!