You can always ask for the extra fee for the extra research. 

  If you have a good relationship with your client I have experienced that they will approve the extra fee.  It is all based on your relationship a lot of the time.  If you don't communicate with your client on a regular basis or develop a good rapport with them then the chances are slim that there will be approval.  When you make that phone call, sound upbeat and confident, tell them about the effort you have already done and what it take to get it done, then ask them for the additional funds.  If they approve then great.  If they don't, is it worth the cancelation of all the work you have already done?  It is a judgment call on each and every search when you ask for the additional funds.  Where do you draw the line, when do you ask for the extra fee, how is your relationship with that client, who is the client, etc...

  Sometimes going the extra distance will build that rapport.  Sometimes it will help, sometimes it won't.  

In the end you have to ask yourself...is this a good client for me and is the extra work worth it? 

Ahh, the joys of running your own business.