Many organizations solve this problem one of two ways
Building a tech team is not feasible if you only need 25-50% of any one position at any given time. The solution becomes to hire one person who can do everything (with varying results) and hope for the best or just outsource the issues as they arise.
Outsourcing issues as they arise is often just as problematic – without a product philosophy and process that is grounded in outcomes and strategic objectives you end up having bugs and issues languish, the product doesn’t evolve and users become frustrated. Interfaces become quickly outdated and you play catch up to recapture clients/users who’ve abandoned the technology in search of something more modern, less buggy, or just fresh.
- IN-HOUSE GURU
Hire an in-house tech guru that can do a little bit of everything. You'll hire someone else for the hard stuff. You need a Jack/Jill-of-all-trades or someone that can do a great job of faking it. This will work if luck is on your side and you can find such a person for the salary you are willing to pay.
- OUTSOURCE AS-NEEDED
Just use your design or dev shop for the big stuff or periodically when things get really bad. Issue RFPs and hope to communicate the need, the ideas, the problems as they filter up to you, assuming you've a way for them to filter into something.
And perhaps the most common approach – Hope for the best. Too often people build some technology and call it done. They don’t plan on expanding and improving. They don’t plan on the cost and effort of care and feeding.