I replaced my ceiling fan in the kitchen. The bulbs are smaller the chandlier type, they required a 60 watt bulb. The bulb keep blowing out, so I went to 40 watt it's still blowing. What could be the problem?

60 Watt is a maximum size, you can use anything less.

Loose connection or bad batch of bulbs. I'll bet the latter. Check the manufacturer lot number.

Check on the back of the package to make sure the bulbs are operable in all positions. There are some brands that will blow out if they are installed base-up, in other words the bulbs hang down

You should start by measuring the voltage at the socket. You may have mis-spliced something when you changed the fan causing the voltage to be other than nominal 120 volts. Also check the splices in the outlet box. There could be a defect in the fan wiring. Measuring the voltage first will help direct you.

Does the fan shake? Does everything else seem normal i.e. fan speed and light brightness?