Should my wife and I file separately?

It depends on why your refund drops.  Is it because she made a lot more or had too little taxes withheld? If you are mostly concerned with your refund alone, then filing separately would make sense.  However, she may end up paying in more so the difference between what you are getting back and she is owing may result in a similar net effect. 

 One thing you can do is to use The Tax Estimator to see what is best in your situation. 

Generally, it is better to file jointly, as several credits and deductions are not available to those who file separate. For instance, earned income and education credits cannot be taken if you file a separate return.  If you wanted to itemize your return, you both have to itemize.  You cannot use the expenses twice so one of you may end up having zero or minimal deductions while the other one takes the itemized deduction.  

 However, some people would still rather file separate because their situation makes it better for them to file separately.