Note: Many of these articles are very old, and although the technical information is still relevant the equipment mentioned may not be (for example a Stormy cooker was state of that art in 1995, but not in 2021).
The higher you go the lower the atmospheric pressure. This will effect your stove. With a cartridge stove, which is basically a gas held under pressure, the drop of pressure will cause the gas to bleed out more forcibly. Firstly this has the advantage that you will get a slightly better burn time (if you remove any other negative variables like temperature) and the canister will show a slight increase in performance through it’s life span. On the negative side you can experience ‘blow out’, where the flame is either impossible to ignite, ignites incompletely, or just goes out mid burn for no apparent reason. This is caused by either too much pressure or a lack of oxygen. Blow outs are both frustrating and dangerous. The lack of a flame means that gas is leaking into your atmosphere - which is both toxic and potentially explosive if it is not stopped quickly. On a committing climb you are also faced with the nightmare scenario of loosing large amounts of your fuel, which in the long term means a loss of food and more importantly water if snow has to be melted. As the pressure inside the cartridge drops then blow out should cease - unfortunately by then you’ll have lost gas. Partial ignition or ‘blow out’ may also be caused by a lack of oxygen getting to the flame (a common problem with hanging stoves that feature ventilation holes more suited to sea level use). This is solved by improving ventilation to the flame and increasing the combustion area - the distance between the flame and the pan. This should only be a problem with hanging stoves and usually requires the lifting of the pan supports or drilling more ventilation holes.