In most of the modern standby lamp, there is no relay for switching the power, the transistor will do that work.
But, firstly you should not open the lamp, as you just bought it for 2 months, just claim the vendor as he is responsible for that defect.
If you can open the lamp, in my opinion as per my experience in 2 cases, try to fix it yourself, it is easy and you will ensure what you have.
For my 2 cases, same sympton - dead batteries - for 2 lamps of different models but from the same manufacturer. Although the manufacturer is welknown, but the lamps are suck. The 6V-4.2Ah battery is always overcharged by the voltage of about 7.9V, while as you know for the standby system, battery should be charged by the voltage of about 2.25...2.3V per cell, or 6.8...6.9V for 6V batteries. The result is the battery dies quickly as we have a habit to plug the lamp into the mains all time 24/7.
So, I repaired the charger, and replaced the battery by myself, and the lamps have been in good condition.
nguyennam