A question for professional accountants: How is it possible for a company to show positive net income but go bankrupt?

Cash profit is different from positive net profit.  Company with insufficient cashflow to settle the debts may go bankrupt.

There are quite instances that inspite of companies showing a good profit goes in to liquidation. The most common one being that the company has 'Credit Sales' and fails to collect the dues from its creditors which in turn will make the company to go in to liquidation. 

Overtrading. Poor payables and receivables management, resulting in a lack of liquidity.  High operating costs and insufficient revenue.

in case of

* - Poor liquidity management then can not pay liabilities on time and accumulating debt

******you  can be expected that from the cash flow statement

Bad Debt - affects your cashflow and ability to continue trading

Selling on credits (Not receiving cash instantly),Paying expenses instantly (Cash),Buying Assets to use in business less or more than one year with cash without balancing the transaction through loan or other financing means.

Having few assets that can easily be converted into cash.

large amount of receivables that move to bad debts.

1) bad debts

2) Poor net working capital mgt

3) Poor cost management

4) Shrinking revenue

As mentioned by others, the company is unable to collect their receivables. Another scenario is they intently manipulating their books to show that they company is in good structure to attract more investors, lenders, customers/clients. They can manipulate this books by restructuring of loans receivable of a customers who declared bankruptcy (instead of charging it to bad debts), bloating their receivables by declaring higher sales or not declaring expenses to hide the effects of losing, etc.