Can I recover this sale?

I am new to sales and I would like to know more about why this happened and if it can be saved.

Prospect has a complex set of requirements involving excel, pdf, some database work, reports, etc. they think they need to hire someone for all this.

I come in, tell them how we can do it easily. They are quite interested. They send me the data and the files right away. They say they are interested in our approach and solution. I follow up the next day with the complete solution, including the screenshots of the process and stuff and I share the results that they wanted in the first place.

Then, nothing. I find myself being gaslighted. Why? Where did I go wrong?

EDIT FOR DETAILS:

1)they have the full power to make the purchase.

2) The problem is a recurring one. They will need to solve it on a regular basis.

3) I offered it as a recurring service which they said they preferred to hiring one or more employees.