It is never late to learn. There is an old proverb which says, "A fish is fresh whenever you pull it out of water". The Holy Prophet of Islam (pbuh) says: "It is the bounden duty of every Muslim to seek knowledge. Beware, God loves seekers of knowledge." Also, in another narration, Imam Sadiq (a.s.) says, "Acquiring knowledge is necessary under any circumstances."
The sayings of the Prophet (pbuh) and Imam Sadiq (a.s.) indicate that old age is not a barrier to seeking knowledge. Our great scholars have been seeking knowledge and wisdom until the last moments of their lives. It is said that when Abu Rayhan al-Beruni was on his deathbed, he was visited by a jurisprudent neighbor of his. Abu Rayhan was still conscious, and on seeing the jurisprudent, he asked him a question on inheritance law or some other related issue. The jurisprudent was quite amazed that a dying man should show interest in such matters. Abu Rayhan said, "I should like to ask you: which is better, to die with knowledge or to die without it?"
Although the sayings of the Holy Prophet (pbuh) and that of Imam Sadiq (a.s.) are universal and applicable to all sciences, the religious sciences are of greater importance because acquiring some of the non-religious sciences is simply permissible, some are recommended and some others are necessary whereas acquiring religious sciences is always obligatory. It should be noted that acquiring some religious sciences is an individual duty and acquiring others is a sufficient necessity (wajib kefayee).
One day the Holy Prophet (pbuh) went to the mosque and met two groups of people. One was busy teaching and learning and the other was busy worshipping. Addressing the people in the mosque, the Prophet (pbuh) said:
"Both groups are [busy] doing good deeds. That group is worshipping Allah and this group is acquiring knowledge and teaching the ignorant ones. This group is superior [to the other group] because I have been sent to teach."
Else where in another hadith, the Prophet is quoted as having said:
"Whoever is at the point of death while he is seeking religious knowledge to uphold the religion of Islam, the distance between him and the prophets in Paradise would be by only one degree."
It is therefore never late to start acquiring knowledge especially religious sciences.
Coming to your question, if you mean to say that the Islamic Seminary (Hawzah) does not admit people who have crossed the age limit for an academic career, we must accept that that every educational system has its own specific rules and regulations so as to prevent and misuse and irregularities on the part of some exploiters. You can refer in person to the Admissions Office of the Islamic Seminary and discuss your situation with them. If you are qualified, you will be formally admitted; otherwise you can start getting Hawzah education without enrolment. At present, there are many people who are busy attending classes and studying in the Islamic Seminary (of Qom) without being formally admitted in the Hawzah.
Indeed, some difficulties including the heavy living expenses might engage your mind but there are many prophetic narrations in this regard according to which God, the Almighty, has guaranteed the livelihood and maintenance of the knowledge seeker. The Holy Prophet (pbuh) said:
"Whoever sets out in the morning in search of knowledge, the angels will put him in their shadows; his life will be full of blessing and his sustenance will not decrease."
Of course, you can engage in some part time jobs to earn your livelihood. Not being admitted in the Islamic Seminary will deprive you of facilities and material benefits only. May Allah grant you success.
 - Al-Kafi, vol.1, pg.30, "The Virtue of Knowledge". The Messenger of Allah (pbuh) said:
طَلَبُ الْعِلْمِ فَرِیضَةٌ عَلَى کُلِّ مُسْلِمٍ أَلَا إِنَّ اللَّهَ یُحِبُّ بُغَاةَ الْعِلْمِ".
 - Behar al-Anwar, vol.1, pg.171. Imam J'afar Sadiq (a.s.) said:
"طلب العلم فریضة فی کل حال".
 - Ayin Danishwari, pg.19, (translation of al-murad min sighat al-murid) cited from Ehya Ulum al-Deen, vol.1, pg.80; Behar al-Anwar, vol.1, pg.184, The Messenger of Allah said:
"... کلا المجلسین الی خیر اما هولاء فیدعون الله و اما هولاء فیتعلمون و یفقهون الجاهل هولاء افضل، بالتعلیم ارسلت".
 - Ayin Danishwari, pg.19, cited from Tafsir al-Razi, vol.2, pg. 180. The Messenger of Allah said:
"من جاء ه الموت و هو بطلب العلم الدینی لیحیی به الاسلام کان بینه و بین الانبیا درجة واحدة فی الجنة".
 - For information about admissions in Islamic Seminaries, click on the following link:
 - Behar al-Anwar, vol.1, pg.184. The messenger of Allah said:
"من غدا فی طلب العلم اظلت علیه الملائکة و بورک له فی معیشته و لم ینقص من رزقة"