What happened to Reverend Alden’s wife on Little House on the Prairie?

In the episode The Preacher Takes a Wife, Reverend Alden marries Anna Craig, a widower who attends the church, despite Harriet Oleson’s best attempts to prevent the marriage.  But after the wedding, Anna never appears again in the series, despite Reverend Alden remaining a regular character through the series.  So what happened to his wife?

Anna Craig Alden is only mentioned once again in the rest of the series, in the episode The Faith Healer, which aired about a month later.

This storyline is considered to be one of the plot holes in the series, since Reverend Alden is a main character and there was an entire episode devoted to his marriage, and her death was only made as a passing mention.