The problem with long term bonds - even government ones - is that if current long term interest rates rise the market value if your previously purchased bonds goes down precipitously. It matters not to the secondary market that those bonds must eventually be redeemed at face value, the issue is now, the potential alternative uses if that money, and the worry about what inflation may do to the value of the money you do get back on redemption. So if a run on the bank forces them to sell their government bonds at a loss, they may indeed not be able to cover their depositors accounts.