What causes the complementary copy of an RNA molecule to separate?
First, I want to point out that the RNA world hypothesis is just that - an hypothesis. While it has been shown that it's possible for certain RNA molecules to make copies of itself, this is not a 'normal' function of any RNA.

Edit - to give a clearer answer to the question itself:

After replication of an RNA molecule it may form a stable structure together with its template or it may dissociate. Due to the various possibilities and complexity of RNA structures its almost impossible to predict this, since both the (exact) sequence itself and environmental conditions especially temperature are very important.

More background from the unedited answer:

Whether two complementary strands or RNA (or DNA) bind together is not something that can always be easily answered. For DNA of a given length (in a given environment / buffer) one can more or less predict the temperature at which complementary strands will separate (often called melting temperature), because DNA forms relatively stable helices.
RNA, however, often forms complicated 3-dimensional structures, often involving self-complementary and is not restricted to the typical helices seen in DNA. Trying to predict the resulting 3D structure of RNA molecules is still an ongoing field of research. Some of these structure are quite stable (e.g. in tRNA) but in other cases they can also be very dynamic and change quickly.
In the end it always depends on the RNA sequence, temperature and many other environmental factors.