"it has developed a habit of not switching on as normal electric devices should"
No, that's not normal. Good gear works for much longer. I'd replace it and not change my habits.
Question 2 is a clue worth answering. There is an epidemic of BAD CAPS (see google) that afflicts far too many devices. If I find bad caps I replace those.
I have (in UK) Broadband Wireless G ASDL2 +Router. It is Huawei Echolife HG520b, Hardware version A;1.0
I occasionally switch it off especially when I am away for the week-end or for letting the transformer cool down for the night when I am not going to use the Internet.
I have been using it for about a year, it has developed a habit of not switching on as normal electric devices should, straight after switching on, It takes the best part of two minutes to show power light. Sometimes it does not show light in its power button for a longer period.
Today I switched it on after about ten hours or so, it did not come on. After about ten minutes I picked it up pushed its connections, i.e. power lead, and other connection leads and it came on. It is working fine. This is new to it and it has been happening for the last couple of months. Before that it worked normally. Once it is on it works as well as it ever did.
1. Should I keep it on all the time ,even when I know I am not going to use it for a couple of days or longer?
2.At times, why does it come on a minute or so after switching it on?(without any touching or moving)
3. I have checked fuse from the main nothing abnormal, is there any inside the Router that takes so long to get connected?(It is situated at a place in the house that no one uses, hence no chance of any interference)
I shall be grateful for any helpful suggestions.