I live in a so-called "majority-minority" district which was considered a lock for a minority candidate since its creation. The incumbent has done such a poor job that he came fairly close to losing the election in 2010. The response? They adjusted the lines to pull extra minorities into his district to ensure that would never happen again.
Incumbents tend to enjoy advantages in terms of resources and name recognition that can make them inherently more difficult to beat, even in the absence of race politics.
A local challenger can be further hamstrung by platform elements adopted at the presidential, federal, or state level that are unpalatable within a district (or unpalatable to a significant group living within that district).
There's a further vicious circle at work where a party decides that a seat is unwinnable, and therefore doesn't put any resources into recruiting effective candidates or running more than a pro forma campaign, and therefore finds that the seat is unwinnable, and so doesn't put in any effort...
There are at least two routes around the problem. First, find a credible non-minority candidate who can demonstrate an ability to work with groups (majority and minority ethnicities) within the district. Not only does this require time and effort, but it may also require the candidate to butt heads with the state or federal party. Second, the cynical route is for your party to find a minority candidate of its own. You've just told me that the district has lots of them; can't you find any of them who want to represent the (Republican) party locally?
The downside of that second approach is that you can't go blaming race anymore when the party still loses; you might have to start looking at why your policies are so unappealing to the minority population.