RNA is very less stable as compared to other cellular macro-molecules like DNA and protein, therefore it would be better to extract RNA within 15-20 days after stored in RNAlater solution and preserve your RNA in Tris pH-7.4-8.0, or in a RNA storage solution from Ambion for at least 90 days.For mi-RNA isolation MiR-vana kit will be better choice.
I'm not entirely sure if you are asking how long you can store tumour tissue in RNAlater and still get good quality microRNA from it or if you are asking how long you can leave tumour tissue taken from patients before putting it into RNAlater and still get good microRNA.
If the first question, I have no experience with that specifically for microRNA. I've gotten good total RNA out of tissue stored in RNAlater for several months. It is important though that you put the tissue into the RNAlater and leave it at RT for overnight to allow the RNAlater to permeate the tissue completely (at least that's what it says in the manufacturer's info sheet). If you have big tissue chunks, you need to cut them into smaller pieces, again to allow complete permeation. Long-term storage should be at -80.
For the second question - the sooner the better! Soon means within minutes, as RNA will start to be degraded very quickly. It may not always be possible to get it right in the operating theatre, but there's little point of using the tissue if it has been several hours. Any results you would get from tissue left lying around that long would not reflect what is really going on in the living tissue but reflect what happens in cell death.