Not exactly, it's the government guarantee for certain bank deposits that has fallen away (gradually and transparent manner) since the GFC. You still have a bank guarantee from mostly investment grade Thai banks for your deposits, just no longer a government guarantee. The banks remain responsible for your money deposited with them.
In fact, if you bank with one of the 5 'systemically important banks' in Thailand, then there is no question that the Bank of Thailand/Government would support them in a liquidity crisis.
If big chunk means up to 2MB, then consider Dee Money is probably your best option. The account set up is quite painless, quick and doesn't require a visit to their office. I set up an account with them early this month via online and SMS.