Testing plays an essential and important role in delivering a quality Software. Rigorous testing is needed during development and maintenance. Testing is also required to reduce failures in operational environment.
No matter in which phase of Software Life Cycle the Software is, bug can be introduced. Nobody can say that there exist a bug free software or system in the world. Even if you do lot of testing you can not say the Software has no bug. Yes, you can say, no bug is found during the test cycle you have executed or set of test cases you have executed. The more defect tester found and it is fixed the more quality a Software has.
When bug come in the Software, debugging is needed. During debugging there is also possibility fix has introduced new bugs. This unwanted bugs is overhead for testing. A tester has to run through regression or repeat several test cases.
Bugs can be introduced due to technology or environment change also. Therefore role of testers never die even when Software is running fine for a month or two while its in operation.
Testing is also necessary to get the confidence that everything is good before you release your product to customer.
Therefore, it does not matter in what phase of Software Life Cycle product is Testing is needed. You can also say that till the time Software exist, Testing also exist.