Protein samples that are 5 months old and freeze thawed 1-2 times a week will be heavily degraded, most proteins will only really survive a handful of freeze/thaw cycles at best, many only one or two cycles. You should get new samples if possible. If you haven't aliquoted your antibodies and you are freeze/thawing this too, you should get new antibodies also. Antibodies often don't do well with freeze/thaw cycles either. Most antibodies are fine at fridge temperature for a few weeks, though there are (many) exceptions to this rule.
The solutions and antibodies should be fine otherwise, though if you are remaking your TBST in the same bottle, it could have carry-over contamination.
The secondary incubation could be a bit long, you should be able to get away with 30 min-1 hour, too long will give you high background all over the membrane, not usually in bands, but this can happen too, especially if there is no specific signal. You also don't need to wash between blocking and primary. For non-specific signal you usually want to wash more times and/or use a more stringent wash (higher salt usually, but also detergent sometimes) between primary and secondary.
The peptide incubation step is for validation of your antibody - it is one of the things you can do to prove that your antibody is binding specifically rather than relying on size, as it is well known that many proteins migrate at different sizes than expected in SDS-PAGE. In your case I wouldn't bother with this step yet, unless you can rule out all the other potential problems first.
My first step would be to get someone to replicate your work using your samples. If the other person, who normally gets good results has problems with your samples/techniques, then that's where the issues lie. As you state that another in the lab is only sometimes having similar issues, look for common points between your work and theirs, the problem(s) will likely lie there.