I used to wonder what actually killed them, but apparently it is very slow suffocation due to you becoming so tired that you are unable to find the strength to move your chest muscles to breathe in! Horrible death! .
That was only the case if the legs were broken - with broken legs there's nothing to support the weight of the upper body, meaning that the torso would sag and, as you say, the victim would die of suffication; horrible but on balance not that long lasting, which is why in some cases victims would have their legs broken deliberately.
Otherwise, the victim could last for some considerable time and could expect to die of a combination of exhaustion, dehydration, blood loss, exposure .... not nice and not quick either. It would have been worse if you'd been young, fit and healthy, because you would have lasted longer. Take it away Wikipedia:
The length of time required to reach death could range from hours to days depending on method, the victim's health, and the environment. A literature review by Maslen and Mitchell identified scholarly support for several possible causes of death: cardiac rupture, heart failure, hypovolemic shock, acidosis, asphyxia, arrhythmia, and pulmonary embolism. Death could result from any combination of those factors or from other causes, including sepsis following infection due to the wounds caused by the nails or by the scourging that often preceded crucifixion, eventual dehydration, or animal predation.
A theory attributed to Pierre Barbet holds that, when the whole body weight was supported by the stretched arms, the typical cause of death was asphyxiation. He wrote that the condemned would have severe difficulty inhaling, due to hyper-expansion of the chest muscles and lungs. The condemned would therefore have to draw himself up by his arms, leading to exhaustion, or have his feet supported by tying or by a wood block. When no longer able to lift himself, the condemned would die within a few minutes. Some scholars, including Frederick Zugibe, posit other causes of death. Zugibe suspended test subjects with their arms at 60ｰ to 70ｰ from the vertical. The test subjects had no difficulty breathing during experiments, but did suffer rapidly increasing pain,which is consistent with the Roman use of crucifixion to achieve a prolonged, agonizing death.
