The answer like always is that everything depends - so is case dependent as you put in your question. I'm not aware that it regularly increases over time, unless the issues get more complicated over time. The most common model is paying by the hour (or sub-hour increment. If you are working with a top-tier silicon valley law firm on IP issues something else complex, you can pay several hundred dollars an hour, or a hundred or two for advice on privacy policies, or less than that for easy work they can punt to an associate. Other arrangements are possible if you have a relationship with the firm or lawyer; like taking options in lieu of cash; or a retainer (fixed price per month). And now more and more standard documents are available online, which might take many of the costs way way down:
http://www.seriesseed.com/posts/2010/02/series-seed-financin...If you can say more about your issue, you might get better feedback - it really is very dependent on the situation.
Hope this helps a little.