Short answer: Yes you can culture HeLa cells indefinitely.
This is the first cancer cell line and has been around since 1951 and has been cultured ever since in thousands of labs. They grow even better than we'd all like, as s large percentage of cell lines in use in cancer research are actually contaminated by HeLa.
However, of course, they may mutate/evolve over the course of time and your HeLa may absolutely be not my HeLa. But that's a different story...
Hi, as Wassim has pointed out there is a limit to subculturing of all cell lines due to the accumulation of mutations. Some journals are even requesting cell lines are authenticated by DNA profiling. It is good to freeze down numerous early passage numbers when you get the cells so after a few passages and experiments you can get out a fresh batch with low passage number. People make the mistake of starting passage number as 1 when taken out of liquid nitrogen, this is not correct as it has usually been through numerous passges before hand and mutations could have occurred.
Dear colleagues, I am agree with the first answer and I recomend the book of Rebecca Skloot untitled "The Imortal Life of Henrietta Lacks, HeLa": This book tells the story about the discovery of the HeLa cels in romanced manner! Henrietta was a poor black tobacco farmer cells taken without her knowledge in 1951, became one of the most important tools in medicine, vital for developing the polio vaccine, cloning, gene mapping, and more. This discovery raises ethical discussion in Medicine.