There are (at least) two approaches to this issue.
The first approach is to say that wave-function collapse never happens. (This is often referred to as the Many Worlds interpretation of quantum mechanics.) Under this approach, the paradox is avoided, since collapse never happens. All measurements are reversible in principle, but measurements conducted with a large measuring device are irreversible in practice for pretty much the same reason that other thermodynamic processes such as friction are irreversible. However, without frequent collapses to simplify things, the wave-function of the universe gets incredibly complicated as it evolves over time, simultaneously containing an exponentially large number of parallel realities.
The second approach is to say that collapse does happen at some point. (The Copenhagen Interpretation) People disagree about where this point is. For example, one hypothesis is that if a large enough number of particles are correlated to the outcome of your experiment, then the wave-function collapses. This would explain why measuring devices made of many atoms cause decoherence. Experiments can be done to put lower bounds on the number of particles this requires. There are many other theories in this category as well. For example, I remember reading about a hypothesis which claims that wave-function collapse is somehow related to gravity. The hypothesis that consciousness causes wave-function collapse is just one of the many in the Copenhagen basket, and much like the hypothesis that collapse is caused by oranges, there is no really strong reason to believe it.
It's important to remember that we still don't really have definitive evidence of wave-function collapse, so all of this is highly speculative. But the question of what happens if we apply the laws of quantum mechanics to the very apparatus we use to do the experiments is a good one, and has been thought about by lots of smart people.
