Should I take action against my apartment complex?

First question is the location of the complex. Is it in a high-crime area where gates are required? If so and if there has been problems with thefts etc which the complex knew or should have known about, then there may be liability. Second question is what is your loss? You have been paid by the insurance company. As a general rule, the insurance company have the right to go against the complex if it was determined that there was liability. This is the right of subrogation (they stand in your shoes). Third question is what would you like done to limit access to the complex when there is construction which requires reasonable access? One remedy would be to sue the complex and request an Order from the Judge requiring that the gates remain secure. This would be difficult and expensive.

Take advantage of your insurance coverage, but notify your insurance of your thoughts about the landlords negligence. If there is an angle worth pursuing, your insurance company will seek reimbursement from the landlord, for the expense of your theft claim. In that manner, your issues are addressed quickly, and any misconduct by the landlord is addressed without expense to you.

I would write them a letter indicating you feel insecure in their supposedly secure complex. and include a bill for your deductible and state that if they fail to reimburse you ..you will report the facts to YOUR insurance company ... so it can sue the complex.

Stop worrying about others and start worrying about yourself. It is not up to you to protect the others, but rather to seek whatever relief is possible to mitigate your loss. The fact that you have full coverage on the motorcycle which was stolen is good, and your insurance company, when they pay the bill, will be seeking to have other people who might be responsible ultimately found liable, which would include the apartment complex. Make the insurance claim and explain all of the circumstances.