When your product appears to be active in your inventory but isn't showing up in search results on Amazon, there could be several reasons for this issue. Here are some steps you can take to troubleshoot and potentially resolve the problem:

1. **Check Listing Status**: Ensure that your product listing is not only in your inventory but also marked as "Active" in the Amazon Seller Central.

2. **Search Accuracy**: Make sure you are searching using the exact product title or ASIN (Amazon Standard Identification Number). Typos or variations in search terms can affect visibility.

3. **Category and Subcategory**: Verify that your product is listed under the correct category and subcategory. Incorrect categorization can affect searchability.

4. **Search Indexing**: Sometimes, it takes a while for Amazon's search algorithm to index new listings. If your product was recently listed, you may need to wait for indexing to complete.

5. **Relevance of Keywords**: Your product's title, description, and backend keywords should be optimized for search. If the keywords are not relevant or not used by customers, your product may not appear in search results.

6. **Sales Rank and Performance**: Amazon's search algorithm considers sales velocity and performance. If your product has low sales or poor reviews, it may not rank high in search results.

7. **Amazon's Search Algorithm**: Amazon's search algorithm is complex and considers many factors, including customer behavior, relevance, and seller performance. Understanding and optimizing for these factors can improve visibility.

8. **Check for Blocks or Suspensions**: Ensure that your account and the product listing are not under any restrictions, blocks, or suspensions that could affect visibility.

9. **Review Amazon's Policies**: Make sure your product and listing comply with all Amazon policies. Violations can result in reduced visibility or removal from search results.

10. **Use Amazon Advertising**: Consider using Amazon's advertising services like Sponsored Products to increase visibility.

11. **Contact Amazon Support**: If you've checked all the above and your product still isn't showing up, reach out to Amazon Seller Support for assistance.

12. **Monitor Performance**: Use Amazon's performance metrics and tools to understand how your product is performing and identify areas for improvement.

By systematically going through these steps, you can identify potential issues affecting your product's visibility on Amazon and take corrective actions.