This question is old but a lot of it still applies.
Risks around VB6 include the following:
- Decreased functionality: without any doubt VB6 is no longer a supported platform. Integrating it with new platforms is every day harder.
- Security Risks: For an internal application the argument that you exposed might be true. However there are some exploits that have been found on th VB6 runtime and due to its unsupported state it makes it a vulnerable target.
- Performance Lag: VB6 was quite performant. You can get some performance benefits from moving to a newer platform but not that much.
- User Interface issues: some VB6 have manage to have an UI that looks modern. So in general I do not see a lot of risks here.
- Limited technical support: this is clearly a risk, specially because there aren't now so many qualified VB6 developers.
- Incompatibility issues: mmm this one depends. It might happend specially due to the lack of support, but it really depends.
Despite the opinions on some of the answers, I definitively believe in the value of conversion tools. Disclaimer I work on a company that sells conversions tools.
Here at my company (https://www.mobilize.net) we have been upgrading VB6 applications to .NET WinForms and to the Web successfully for 20 years.
We think that one of the key elements for a good project comes from planning. We start by creating a BluePrint (see more here https://www.mobilize.net/solution/legacy-solutions/migration-blueprint) which is mostly a detailed inventory of all the assets for the application or for the complete application portfolio.
I also recommend reading blogs like (https://blogs.artinsoft.net/) and there is a free book you can review: https://migrationguide.artinsoft.com/
If your VB6 application is still alive, it means that is is unique and not easy to replace. A rewrite could be an alternative but a migration is