I don't know your toy, so the following may be unhelpful.
Firstly, I'm a strong advocate of "if it ain't broken, don't fix it". In my experience, injectors can last many, many months, or just a few days, before maintenance is required. The duration between servicing depends on sample cleanliness, septum robustness, analyte sensitivity to system activity, column sensitivity to junk, and many other factors.
The preventative maintenance programme should be based on experience. Given that you had a relatively long hassle-free period, I suspect you have inadvertently affected something, most probably introducing either activity or a injector leak during service. Once it's fixed, wait for the next failure before setting preventative maintenence times.
The septa coring is an issue, and I'd switch to coned needles if you aren't already using them. I would also look closely at the septa you are using, and ensure they are the most suitable, with regard to injector temperature, needle type, and resistance to coring. I prefer either multi layer septa or really good quality, low bleed, core resitant, single layer types. Cheap septa will tear and core easily.
I would first ensure that the system isn't leaking around the septa or column connection at injector operating temeperature. If you don't have a leak detector, Snoop ( detergent and water ) can be used - just ensure the system is pressurised, and rinse the Snoop off with distilled water. Then I would condition the system ( column and injector ) at near recommnded isothermal maximum temperature, at least for several hours. I would then inject some blanks, and once the baseline was settled, I'd inject, six to ten times, a test mixture of alkanes, alcohols, and/or your samples, followed by a couple of blanks. I know some many injections manually are a bore, but you need to ascertain the cause of your problems.
I would look at the data for trends, any random RT variation is most likely caused by injector/syringe leaks. A trend of increasing peak sharpness and symmetry with injections is likely to caused by activity, a trend of all peaks increasing area with injection is a sign that there is residual activity, a trend of the higher boiling compounds % area increasing is a sign of discrimination or activity, and you should either keep injecting the mixture, or allow the system to condition for much longer.
Please keep having fun,
Bruce Hamilton