In regarding to the main inquiry which asked “Why Matam by Shias when maximum mourning period is 4 months?”, there would be some various responses from different aspects. Let's survey it briefly from some aspects. Definitely pointing to Qur'an verse(s)/ayah would be sufficient to prove the issue. Let’s pay attention to the verse 84 and 85 of Surah Yusuf as two related matters:
وَتَوَلَّىٰ عَنْهُمْ وَقَالَ يَا أَسَفَىٰ عَلَىٰ يُوسُفَ وَابْيَضَّتْ
عَيْنَاهُ مِنَ الْحُزْنِ فَهُوَ كَظِيمٌ ﴿٨٤
And he turned away from them and said, "Oh, my sorrow over Joseph,"
and his eyes became white from grief, for he was [of that] a
قَالُوا تَاللَّـهِ تَفْتَأُ تَذْكُرُ يُوسُفَ حَتَّىٰ تَكُونَ حَرَضًا
أَوْ تَكُونَ مِنَ الْهَالِكِينَ ﴿٨٥
They said, "By Allah, you will not cease remembering Joseph until you
become fatally ill or become of those who perish." (85)
The verses above-mentioned declare that Jacob was involved in weeping for being away from his son (Joseph)… furthermore there are a related tradition which narrated by Zamakhshari as a Famous Sunni Mofaser (expounder) of the holy Qur'an (And likewise Al-Fakhr al-Razi) who narrated:
Joseph asked Gabriel concerning the time when his father was crying
and sorrowing, then he responded “it took 70 years (he was crying for
70 years), and asked him concerning the reward of his crying, he
responded “his crying reward equals 70 martyrs.
Besides, there are many traditions concerning the mentioned issue from Shia Imams; For instance, it has narrated that Imam Sajjad (Zain al Abedin) (a.s.) as the fourth Imam of Shia, permanently he was sorrowing for the event of Ashura during his Imamate period; he cried too much for the mentioned event that he was considered and was titled as “Boka’een” who was counted as the persons who cry a lot.
- Tafseer al Keshaf, Zamakhshari, 2th edition, pg. 497, and Tafseer al
Kabir, Al-Fakhr al Razi, Vol.18, pg. 193 (in regard to verses 84 & 85
- تفسير الكشاف، زمخشري، نسخه(التحریر)2، ص497 و تفسير الكبير، الفخر
الرازي، ج18، ص193، ذيل آيات 84و85
- Wasa’elul-Shia, vol. 2, pg. 922.