Is it permissible to distinguish Ramadan by performing night prayers (Qiyam al-Layl) to the exclusion of other days?

Night prayer (Qiyam al-Layl) is a confirmed Sunnah, both during Ramadan and outside of it. A Muslim should always strive to observe it. As for someone who limits night prayer only to Ramadan, they have missed out on much good, yet they have still attained great good, for the Prophet, peace and blessings be upon him, said: "Whoever stands (in prayer) during Ramadan with faith and expecting Allah's reward, all his past sins will be forgiven."