if the moment you place an order there is a supply of shares, you can buy them, except sometimes between the 16th and the 19th of the month when nothing happens, like the game is frozen.
if you place an order but no shares are available (no supply), the order will be there for 2 months then it will be canceled automatically.
if you own at least a share, you can change from your portofolio to buy automatically up to the desired percentage of shares of a corporation. the auto buying and selling of shares is set to 10% each game month.
between the 1st and the 7th of the month, buying shares is almost instant so if no demand for shares, you can sell and buy 2 batches per game day if shares are sold or bought by C3 countries. shares are bought by C3 countries if p/e is below 45.
if you see there are shares in supply, so someone is selling, but your buy order is not fulfilled, than there is a bug