Only way I can think of avoiding this is
1) DO NOT promise fixed rates, and get people used to them fluctuating based on your returns (even if they vary by 0.01%). Not only will this make it easier to lower rates if you have to, but the changes in the rate will at least give "investor" some signal as to how your business is going
2) Be open about your holding as much as you can. At the least, tell people how much you have in reserves v.s. how much you have lent out. This will at least give them an idea of how risky you are should a bank run occur.
+1 (finally someone recognises the basics).
For the newbies trolling the lending section, they might be interested to know rates have roughly halved in the past six months. Personally I've already done one reduction and was planning a second before deciding to change the future direction of StarfishBCB.