When an Imam passes away after transferring the office of Imamah to his successor does he seize to be Allah's hojjat, as well as Imam?
Being a Hojjat is irrelevant of being passed away or not. For example Quran is a Hojjat for Muslims and is Hojjat for always.
If a person or a thing is a Hojjat for Muslims so all Muslims have obligation to obey and follow it/him.
Prophet Muhammad (SAWW) is a Hojjat for Muslims. So all Muslims have obligation to obey and follow him. And if do not obey him it is recorded as a sin and will be questioned at Judgement day.
So basically being Hojjat is irrelevant of being living or passed away. The words and sayings of a Hojjat person is Hojjat for always. We do not need the physical body of a Hojjat person like the Prophet (SAWW). In fact we should obey his sayings which are alive always.
Also according to Quran the Prophet (SAWW) and infallible Imams never die and we are not permitted to call them dead:
And never think of those who have been killed in the cause of Allah as dead. Rather, they are alive with their Lord, receiving provision. http://tanzil.net/#3:169
They are alive always and see and hear us:
And say, "Do [as you will], for Allah will see your deeds, and [so, will] His Messenger and the believers. And you will be returned to the Knower of the unseen and the witnessed, and He will inform you of what you used to do." http://tanzil.net/#9:105
It is clear that regular believers do not see the deeds of people. "The believers" in this verse means prophet (SAWW) and Ahl-al-Bayt. There are many hadith regarding this verse saying this verse is about Ahl al Bayt and the angels deliver deeds of people to them and they see deeds every week.
Hojjat is Hojjat for always. As an example lets the person X established the Constitution law of a country. When that person dies the Constitution loses its validity? No, in fact the validity is independent of the death of the person who delivers it to humans.
Every single saying of any of infallible Imams of Ahl-al-Bayt is Hojjat for all Muslims based on Hadith of the two weighty things and many verses of Quran and Muslims will be questioned about disobeying them at Judgement day.
The concept of Hojjat in Islam should be understood well.
References and more study: