Do you know of a script to auto-delete the index and recreate it by a schedule instead of manually?
I'm not familiar with any problem of full-text indexes growing over time. What version of Notes are you using?
I don't think it should be necessary to delete and recreate it. But in Notes 6, you can use the RemoveFTIndex and UpdateFTIndex methods to delete and recreate the index. In earlier versions, I'm not sure -- you could try just deleting the ".ft" directory, which should force the server to recreate the index the next time it's used (or when your agent calls UpdateFTIndex).
You might want to look at ways to limit the number of documents and the number of modifications and document creations, which can cause performance problems in all aspects of operation, not just full-text searches. Often I see applications that can be streamlined by combining several forms into a single form, reducing the number of documents considerably. This is particularly the case where the Notes database has been made overly "relational" in structure, with parent documents and subsidiary "line item" documents to reproduce the structure of a one-to-many relationship from a relational database. You may be able to use a table editing tool to reduce this to one document containing a multi-row table. You might also think about archiving old documents.