For clarification, your employer does not sponsor your HSA. Your employer probably provides your HDHP insurance policy, but the HSA itself is totally separate, in a way similar to an IRA. And like an IRA, the HSA belongs to you, not to your employer - even if your employer helped you set the HSA up.
This means that when you leave your current employer, you do NOT have to cash out your HSA - in fact, it is a bad (and expensive) idea to do so.
You can continue to pay for qualified medical expenses from your HSA even if you no longer have HDHP coverage. And if you take a new job that also has HDHP coverage, then you can start contributing to the HSA again (you can't when you have no HDHP coverage).
Note that in this latter case, you do NOT have to create a new HSA with the new employer; you can still use and contribute to the old one. However, some employers won't send payroll contributions to any HSA but the one they help set up - in this case, just set up the new HSA. You can have multiple HSAs at the same time. (note that your annual HSA contribution limit is for the aggregate of all your HSAs).
If the fees are eating you up by having two HSAs, then call your old HSA custodian and ask to do a trustee to trustee transfer of the money in the old HSA to the new HSA; this action will have no tax consequence for you. Then, when the old HSA is empty, you can close it and start using only the new one.
