Yes, it's indeed a problem with the waterproofing. There are two main causes:
Any outdoor gear must be bone dry before you store it. It also needs to be stored in a dark, dry, and ventilated place. If a tent, never store it in its stuff sack, instead use a dirty laundry mesh bag (for a small tent) or if a bigger tent, jacket, backpack, use a giant mesh bag for corn, beans, etc. You can get those free at your local grocery (pictures at the bottom). However, the best for a backpack is to hang it just like that.
No matter what, the waterproofing coating (inside), and the exterior DWR will deteriorate over the years (DWR has a much faster deterioration rate)
DWR is NOT waterproofing
Many have that wrong, including several magazines... DWR stands for Durable Water Repellant. As you can see, it's Repellant and not Waterproofing. DWR is increasing the “contact angle” or “surface tension” created when water touches a textile. DWR will make water pearl and slide off instead of sticking to your gear/jacket. DWR is to be applied outside, and waterproofing on the inside.
The most common waterproof coatings used in tents and backpack are: polyester urethane (PU), polyether urethane (PE), and silicone, and combinations thereof. You can read a very good article about that to help you choose between PU, PE, and silicone to re-waterproof your backpack: https://www.slingfin.com/blogs/the-beta/fabric-coatings-101-pu-vs-pe-vs-silicone
Step-by-step process for your backpack
a) Remove the old coating by using a sponge (or a rag) and rubbing alcohol
b) You need to make sure your backpack is 100% clean. So wash it but do NOT use any laundry detergent or anything like that because it will leave residues and the coating won't "stick" properly. There are three main products for that: Tech Wash (from Nikwax) and Tent+Gear Cleaner (from Grangers). And the third one is the good old Castile Soap (any brand will do).
c) For waterproofing, it's best to use the same coating as used by the manufacturer. However, this may be very hard to find in your case. You can choose between polyurethane or silicone. One of the best sealant for polyurethane treated fabrics is Gear Aid Seam Grip + TF Tent Fabric Sealant. Silicone treatment is a bit trickier so I suggest you go for the PU coating.
d) Sealing the seams: that part is often forgotten! For this, the best is to use Seam Grip WP (from Gear Aid) or Seam Grip FC (also from Gear Aid) if your backpack is treated with silicon.
DWR on the outside
The final touch is to add a DWR on the outside. For this, I suggest TX.DIRECT (from Nikwax). Just apply as indicated on the bottle.
a) remove the old coating
b) apply the waterproofing coating inside the backpack
c) seal all seams
d) apply the DWR on the outside
e) no matter what, always use a plastic bag inside!
f) if you have a double zipper, never close with both at the top, always on the side.
Don't hesitate if you have any questions.