What is the number of days since the last time i went to the gym in which i will start feeling weaker and start losing the progress I've made?
You may be interested in my response to a similar question I answered: Will I lose gains in this situation? . Since each of us is an individual, no one can say for sure how long it would take for you, specifically, to “lose progress”. However, if you look at the study results mentioned in my answer, you’ll see that there are some guidelines that may shed some light and help you understand your individual situation.
You can search studies about "residual training effects" for different sport performance parameters e.g. aerobic endurance, maximal strength, ...
Average numbers suggest aerobic endurance adaptations last for about 30 days, strength also. Anaerobic glycolytic adaptations last for about 18 days, strength endurance about 15 days and maximal speed 5 days.
These numbers explain the idea behind periodizing for competitions. If you train for the 100m dash then your training program shall allow for maximal speed training near your competition while GPP shall be placed at the beginning of the season.