It depends on what is implied by over time in the question.
Virus may become more deadly (or otherwise harmful) simply due to a random mutation. However, virus does not specifically aims at harming the host - rather the negative consequences for the host's health are a byproduct of the virus hijacking and killing the host cells. This can be, e.g., due to the toxins generated during the viral replication, or due to the new virions bursting out of a cell and thus destroying it, or because of the overreaction of the host's immune system. E.g., HIV preys at the immune CD4+ cells, whose count eventually drops below the critical level, making the host susceptible to opportunistic diseases.
Thus, in a short run virus becomes more harmful/lethal, as the byproduct of being more successful in replicating and propagating itself. However, in the long run such success harms the virus, since, as an obligate parazite, it cannot exist without a host. Reduced number of hosts means reduced possibilities for virus to replicate. A virus that kills all of its hosts goes extinct. The viruses that continue exist do so either because they have reached an endemic equilibrium with their host or because they can survive in a host of different species, occasionally spilling into human population (like Ebola).