I'm facing a similar question right now, myself! Again. I have already done exactly this: taken a product to market on my own after having developed it for a client who let me keep the IP. I would consider it successful, as it sustained me and my family for about 8 years and concluded with a successful sale to a competitor who I admired and felt good about selling to.
It is a tempting opportunity to have someone else pay for the development of a product that you can re-sell, but it will fundamentally change your business model (from services to product) and you may find it a bigger change than you originally anticipated.
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Here are a few areas I would explore:
1) YOUR DNA - Is your organization's "core competency" (i.e. collection of resident skill sets, passions, and qualifications of your company) geared more towards project management or product development? If you are naturally "better" at short-term high-value projects, then you will need to develop or acquire skills in product development in order to take the new app to market. Remember that maintaining software for end-user consumption (whether SaaS or packaged SW) is very different than building an initial release per client spec.
2) THE MARKET - What has been the result of your market research for inventory maintenance management apps? Is the market saturated already? Will this be a high-margin niche product or low-cost commodity app? Do you have ready access to likely markets and buyers? Will your existing client be a champion and advocate for you in the marketplace? The fact that your existing client is willing to pay you for it indicates demand to some degree, but you should do a meaningful market analysis before making a decision.
3) YOUR GOALS - Do you have an "exit strategy" from your services company already? I can only make assumptions about your current business, but if you like the idea of a "lifestyle" business that you never intend to capitalize or liquidate, then sticking with services is a good option. If, on the other hand, you have been contracting out development services in hopes of finding that idea you can productize, then this opportunity may BE your exit strategy!
4) THE OPTIONS - Of course, you could always do "both": keep the development services going while the product takes shape and launches. This could have the benefit of continued cash flow to your company to support the product, but also carry the risk of stretching your resources too thin and/or the organization becoming distracted. Make sure you consider how to fund those extra expenses (i.e. marketing, sales, end-user support, infrastructure, etc.) associated with launching a product.

These are just a few questions to get you thinking. In my case, it will come down to a fairly rigorous financial and risk analysis. I will assess the marketplace (demand, competitors, positioning) as well as I can, estimate the costs associated with launch and promotion, and then negotiate the terms with the client to stretch the opportunity runway as long as possible. If I am convinced that it will pay off, then you can expect to see me launching my next venture around February 14, 2015!

In the meantime, I would be happy to discuss your specific situation in more detail if you would like to chat by phone or email. Good luck and never stop having FUN!