Signs of depression and anxiety should not be ignored if they linger for too long. If the person has remained depressed for a period which is over a few days then he or she has a mental problem and needs help in the form of proper treatment. Delaying treatment would only mean making the person more miserable and it would take longer to make them comfortable even if it is not possible to cure them. Ordinary depression which is for an incident which has caused it will ease and antidepressants could help the person tide over a difficult period. However, it the person has a mental imbalance like a bipolar disorder then the treatment has to be continuous though the dosage has to be reviewed periodically.
Many who have signs of depression refuse to admit it and do not agree to counseling and treatment. Often even the near and ones do not want to admit that one of their kith and kin has a mental disorder. This makes treatment a difficult proposition and the person may end up in a bad state.
If on the other hand there is a problem which is causing the depression and anxiety it would be best to face it and discuss it with someone close to you so that you can sort things out and not suffer in silence. Marital problems should be sorted out with the spouse; financial problems with those you owe money to or to a bank to bail you out. Sometimes it is the job that is causing the stress and anxiety and it would be best to discuss it with your immediate boss at work to see how things could be changed to make you more comfortable.