I think it's definitely possible that a constantly depreciating currency may deter investors because it is a sign of a weakening economy, but be careful saying "force", because nothing is forcing them to do anything. It all depends on their future expectations, and whether they think the economy will recover.
You should also note that FDI isn't readily removable to shift to other countries, only portfolio investment is. However, as grouchygigi said, any form of investment would become cheaper, driving demand. Also, rising import prices as a result of currency depreciation can lead to imported inflation, which central banks would respond to by increasing the cash rate. This causes increases in interest rates and thus the rate of return on investment, which can encourage speculators to invest, boosting capital inflows.