You can read some testimonials in this thread.
You may also browse the ObjectDB forum and issue tracking to get impression. ObjectDB is stable and robust, but naturally like any other software, issues are reported occasionally. But as you can see in the forum and in the issue tracking - bugs are usually fixed very quickly as soon as they are found.
ObjectDB is in use successfully in critical and sensitive systems in the banking and defense industries.
But before you decide to use ObjectDB in your project you should probably take it for a drive test, to verify that it matches your specific project needs.
ObjectDB - Fast Object Database for Java (JPA/JDO)