If people want to gather to perform Qiyaam al-Layl in the mosque in congregation at times other than Ramadaan, this is a kind of bid’ah.
But there is nothing wrong with a person praying it in congregation at times other than Ramadaan in his house occasionally, because the Messenger (peace and blessings of Allaah be upon him) led Ibn ‘Abbaas, Ibn Mas’ood and Hudhayfah ibn al-Yamaan in congregation in his house. But he did not do that as a regular Sunnah (Sunnah raatibah) and he did not do it in the mosque.
See al-Sharh al-Mumti’ by Ibn ‘Uthaymeen, part 4, p. 82
It should be noted that this jamaa’ah (prayer in congregation) which takes place at times other than Ramadaan should not happen by agreement or prior announcement. If it so happens that a Muslim sees another Muslim praying Qiyaam al-Layl and he joins him without prior agreement – as happened in the hadeeth of Ibn ‘Abbaas, for example, when he woke up and joined the Prophet (peace and blessings of Allaah be upon him) one night – there is nothing wrong that. But if it is a meeting by prior agreement to perform Qiyaam al-Layl on a regular basis, almost every night – as described in the question – this is bid’ah, as stated at the beginning of the answer.
We will quote the hadeeth of Ibn ‘Abbaas (may Allaah be pleased with him). He said:
“I stayed overnight in the house of my maternal aunt Maymoonah. The Prophet (peace and blessings of Allaah be upon him) slept for a part of the night… and during the night, he got up and performed a light ablution from a hanging water skin, and stood up for the prayer. I, too, performed a similar ablution, then I went and stood on his left. Perhaps Sufyaan said, on his left and he drew me to his right. He prayed as much as Allah wished, then he lay down and slept until the sound of his breathing could be heard. Later on the muezzin came to him and told him that it was time for prayer. The Prophet (peace and blessings of Allaah be upon him) went with him for the prayer without performing a new ablution.” Sufyaan said to 'Amr that some people said, “The eyes of the Messenger of Allaah (peace and blessings of Allaah be upon him) sleep but his heart does not sleep.” ‘Amr said, “I heard ‘Ubayd bin ‘Umayr saying that the dreams of Prophets were wahy (revelation), then he recited the verse (interpretation of the meaning): ‘he [Ibraaheem] said: “O my son! I have seen in a dream that I am slaughtering you (offering you in sacrifice to Allaah)”’ [al-Saaffaat 37:102].”
(Narrated by al-Bukhaari, 138