Your site looks great and the product seems substantial and well thought out. However, as you indicated, finding out if there is a sweet spot for what you do is not always easy. Take a step back and, at a generic level, define what your company is really good at and what forms the backbone of how you deliver value. Is this the complete set of things that you need to be good at to win in the business as you have defined it?
Next, define your value proposition for each of your key constituents (schools, tutors, tutees) along with the criteria they use to evaluate the offering's attractiveness to them. Define personas and use cases within each constituent group to identify who you are best positioned to satisfy. For each constituent, list the positive, negative and puzzling things you have heard in their feedback or observed in their actions.
Doing this for each of your current and past target market initiatives (B2C and B2B) may help you develop new insights. What is different from your original hypotheses? When you look at key metrics or assumptions in your model, are there any in which small improvements could lead to significantly better performance (traffic, referrals, trial, conversion, time to fulfill, repeat usage, etc)? What else might you do to improve performance at the key leverage points? What questions should you be asking to gain further insight on how to move the needle?
Two-sided P2P marketplaces are fundamentally challenging. In your case, you need to generate enough supply and demand to satisfy both tutors and tutees. A B2B sponsorship model has the potential to address this quickly and effectively if they actively embrace it and feel compelled to make it work. Are your school customers being proactive in their support for your platform? Are they referring your solution or generating enough awareness to interest and engage a high proportion of potential tutors and tutees? Are you meeting the schools' expectations and are they seeing a positive ROI? If you are losing tutors and/or tutees to some form of direct or indirect competition, what are the implications for your business (features, pricing, promotion, awareness, expectations, reducing "friction," etc.)?
It would be helpful to know what feedback and insights you have received directly from participants. What has this told you about your (real or perceived) ability to meet expectations, overcome barriers to use, generate referrals and drive repeat/retention?
At the end of the day, if you feel you need to look for opportunities to "pivot" the business, start by referring back to the core strengths that I mentioned in the first paragraph. Are there other applications and markets where you could provide value by redeploying a version of your platform and leveraging these core strengths?
I'd be happy to talk through any and all of the above and would welcome the opportunity to learn more about your team and business.