An immediate problem with requiring an eternal life for meaning is that it only puts off the question. One could live eternally in a totally purposeless existence, like Sisyphus, pushing a boulder up a hill only to have it roll to the bottom again for you to start over ad infinitum. So an eternity does not automatically confer meaning to existence. But that does not directly answer the question of whether meaning is possible in a finite life.

Some people think that being part of a grand plan, a higher purpose, is what gives a life meaning. Modern science paints a picture where humans are but one step in a long process full of chance, and not the realization of some evolutionary 'ultimate goal'. The problem with requiring a greater plan for meaning is that it again only puts off the question. An eternal life could easily lack any such plan; and if being part of a greater purpose is what does confer meaning, it could just as easily confer it to a finite life as an infinite one.

There are lots of different views on the question of what does make life meaningful, and I don't claim to have the answer myself. Perhaps we create our own meaning, based on what makes us happy, and our seeking after that happiness and understanding it. Perhaps in setting goals for ourselves (and I don't mean just short term goals like exercising daily or passing a class) and trying to reach those goals, we create a purpose that confers some meaning to our lives. Perhaps making an impression, passing on our thoughts, our ideas, even our genetic material to other people (through books, 'memes' or even just having children) gives our lives meaning by changing the world, having a real effect. Perhaps simply in virtue of being a part of something bigger and more diverse than ourselves (a society, the human species, sentience, or life itself!), we are inextricably tied to a larger and meaningful whole. Another way to look at it is that a finite life confers meaning because there are limits, risks, a beginning and an end - all of which seem to be integral to the sense of satisfaction and accomplishment which we humans so closely associate with meaning.

The reasonable conclusion seems to be that meaning (nebulous as the word might be in this context) in our human lives, if it can be achieved at all, is something that can be achieved without any need for eternity, for a life after death. Savor life while you have it, and the fact that there is an end makes it all the more precious.