又doesn't necessarily used in past tenses.
- 又芳香又美味 (also Fragrant and delicious).
- 他又成功了 (He succeed again!)
As you can see, it is used in repetitive action or an emphasis of a subject.
In the case of 今天又没有上课, he is not attending class today again! or he didn't attend the class today again!
You probably knew he is playing truant and not coming to class today hence you use 又 for repeated behaviour. He did it on yesterday and he did it again on today and probably also the day after next.
If you wanted to use 再 in this context. I would suggest to do it this way:
他除了昨天，就没再来上课了. (He didn't attend class anymore except yesterday.).
So you only knew he wasn't in class then and aren't sure whether he will did it again.
I hope I am not confusing you.
Just my 2 cents worth.